1.D6

    order := 12,
    length := 40,
    subgroup := MatrixGroup(9, Integer Ring) of order 2^2 * 3
    Generators:
        [ 2  1  0  1  0  1  0  0  0]
        [-1  0  0 -1  0 -1  0  0  0]
        [ 0  0  0  0  1  0  0  0  0]
        [-1 -1  0 -1  0  0  0  0  0]
        [ 0  0  1  0  0  0  0  0  0]
        [-1 -1  0  0  0 -1  0  0  0]
        [ 0  0  0  0  0  0  1  0  0]
        [ 0  0  0  0  0  0  0  1  0]
        [ 0  0  0  0  0  0  0  0  1]

        [ 2  1  1  0  1  0  0  0  0]
        [-1  0 -1  0 -1  0  0  0  0]
        [-1 -1  0  0 -1  0  0  0  0]
        [-1 -1 -1  0  0  0  0  0  0]
        [ 0  0  0  1  0  0  0  0  0]
        [ 0  0  0  0  0  1  0  0  0]
        [ 0  0  0  0  0  0  1  0  0]
        [ 0  0  0  0  0  0  0  1  0]
        [ 0  0  0  0  0  0  0  0  1]

        [ 2  0  0  1  1  1  0  0  0]
        [ 0  0  1  0  0  0  0  0  0]
        [ 0  1  0  0  0  0  0  0  0]
        [-1  0  0  0 -1 -1  0  0  0]
        [-1  0  0 -1  0 -1  0  0  0]
        [-1  0  0 -1 -1  0  0  0  0]
        [ 0  0  0  0  0  0  1  0  0]
        [ 0  0  0  0  0  0  0  1  0]
        [ 0  0  0  0  0  0  0  0  1]>

Orbit type:{4,12}

Orbit:
1
{@
    Mod: ( 1 -1  0  0  0 -1  0  0  0),
    Mod: ( 1  0 -1  0  0 -1  0  0  0),
    Mod: (0 0 0 0 0 1 0 0 0),
    Mod: ( 1  0  0 -1 -1  0  0  0  0)
@}
Intersection Matrix:
[-1  0  1  1]
[ 0 -1  1  1]
[ 1  1 -1  0]
[ 1  1  0 -1]
Stabilizer Group Name:
C3
MatrixGroup(9, Integer Ring)
Generators:
    [ 2  1  1  0  1  0  0  0  0]
    [-1  0 -1  0 -1  0  0  0  0]
    [-1 -1  0  0 -1  0  0  0  0]
    [-1 -1 -1  0  0  0  0  0  0]
    [ 0  0  0  1  0  0  0  0  0]
    [ 0  0  0  0  0  1  0  0  0]
    [ 0  0  0  0  0  0  1  0  0]
    [ 0  0  0  0  0  0  0  1  0]
    [ 0  0  0  0  0  0  0  0  1]

2
{@
    Mod: ( 1  0  0  0 -1 -1  0  0  0),
    Mod: ( 1 -1  0 -1  0  0  0  0  0),
    Mod: (0 0 1 0 0 0 0 0 0),
    Mod: ( 1 -1  0  0 -1  0  0  0  0),
    Mod: ( 1  0 -1 -1  0  0  0  0  0),
    Mod: ( 2 -1 -1 -1 -1 -1  0  0  0),
    Mod: (0 0 0 1 0 0 0 0 0),
    Mod: ( 1  0  0 -1  0 -1  0  0  0),
    Mod: ( 1  0 -1  0 -1  0  0  0  0),
    Mod: (0 1 0 0 0 0 0 0 0),
    Mod: ( 1 -1 -1  0  0  0  0  0  0),
    Mod: (0 0 0 0 1 0 0 0 0)
@}
Intersection Matrix:
[-1  1  0  0  1  0  0  0  0  0  1  1]
[ 1 -1  0  0  0  0  1  0  1  1  0  0]
[ 0  0 -1  0  1  1  0  0  1  0  1  0]
[ 0  0  0 -1  1  0  0  1  0  1  0  1]
[ 1  0  1  1 -1  0  1  0  0  0  0  0]
[ 0  0  1  0  0 -1  1  0  0  1  0  1]
[ 0  1  0  0  1  1 -1  1  0  0  0  0]
[ 0  0  0  1  0  0  1 -1  1  0  1  0]
[ 0  1  1  0  0  0  0  1 -1  0  0  1]
[ 0  1  0  1  0  1  0  0  0 -1  1  0]
[ 1  0  1  0  0  0  0  1  0  1 -1  0]
[ 1  0  0  1  0  1  0  0  1  0  0 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1

2.C3⋊C4

    order := 12,
    length := 40,
    subgroup := MatrixGroup(9, Integer Ring) of order 2^2 * 3
    Generators:
        [ 2  0  1  1  0  1  0  0  0]
        [ 0  0  0  0  1  0  0  0  0]
        [-1  0 -1 -1  0  0  0  0  0]
        [ 0  1  0  0  0  0  0  0  0]
        [-1  0 -1  0  0 -1  0  0  0]
        [-1  0  0 -1  0 -1  0  0  0]
        [ 0  0  0  0  0  0  1  0  0]
        [ 0  0  0  0  0  0  0  1  0]
        [ 0  0  0  0  0  0  0  0  1]

        [ 2  1  0  1  1  0  0  0  0]
        [ 0  0  1  0  0  0  0  0  0]
        [-1  0  0 -1 -1  0  0  0  0]
        [-1 -1  0  0 -1  0  0  0  0]
        [-1 -1  0 -1  0  0  0  0  0]
        [ 0  0  0  0  0  1  0  0  0]
        [ 0  0  0  0  0  0  1  0  0]
        [ 0  0  0  0  0  0  0  1  0]
        [ 0  0  0  0  0  0  0  0  1]

        [ 2  1  1  0  0  1  0  0  0]
        [-1  0 -1  0  0 -1  0  0  0]
        [-1 -1  0  0  0 -1  0  0  0]
        [ 0  0  0  0  1  0  0  0  0]
        [ 0  0  0  1  0  0  0  0  0]
        [-1 -1 -1  0  0  0  0  0  0]
        [ 0  0  0  0  0  0  1  0  0]
        [ 0  0  0  0  0  0  0  1  0]
        [ 0  0  0  0  0  0  0  0  1]>

Orbit type:{4,12}

Orbit:
1
{@
    Mod: ( 1 -1 -1  0  0  0  0  0  0),
    Mod: (0 0 0 0 0 1 0 0 0),
    Mod: ( 1  0  0  0 -1 -1  0  0  0),
    Mod: ( 1  0  0 -1  0 -1  0  0  0)
@}
Intersection Matrix:
[-1  0  1  1]
[ 0 -1  1  1]
[ 1  1 -1  0]
[ 1  1  0 -1]
Stabilizer Group Name:
C3
MatrixGroup(9, Integer Ring)
Generators:
    [ 2  1  0  1  1  0  0  0  0]
    [ 0  0  1  0  0  0  0  0  0]
    [-1  0  0 -1 -1  0  0  0  0]
    [-1 -1  0  0 -1  0  0  0  0]
    [-1 -1  0 -1  0  0  0  0  0]
    [ 0  0  0  0  0  1  0  0  0]
    [ 0  0  0  0  0  0  1  0  0]
    [ 0  0  0  0  0  0  0  1  0]
    [ 0  0  0  0  0  0  0  0  1]

2
{@
    Mod: ( 1 -1  0  0  0 -1  0  0  0),
    Mod: ( 1 -1  0 -1  0  0  0  0  0),
    Mod: (0 0 1 0 0 0 0 0 0),
    Mod: ( 1 -1  0  0 -1  0  0  0  0),
    Mod: ( 1  0 -1 -1  0  0  0  0  0),
    Mod: ( 2 -1 -1 -1 -1 -1  0  0  0),
    Mod: (0 0 0 1 0 0 0 0 0),
    Mod: ( 1  0  0 -1 -1  0  0  0  0),
    Mod: ( 1  0 -1  0  0 -1  0  0  0),
    Mod: ( 1  0 -1  0 -1  0  0  0  0),
    Mod: (0 1 0 0 0 0 0 0 0),
    Mod: (0 0 0 0 1 0 0 0 0)
@}
Intersection Matrix:
[-1  0  0  0  1  0  0  1  0  1  1  0]
[ 0 -1  0  0  0  0  1  0  1  1  1  0]
[ 0  0 -1  0  1  1  0  0  1  1  0  0]
[ 0  0  0 -1  1  0  0  0  1  0  1  1]
[ 1  0  1  1 -1  0  1  0  0  0  0  0]
[ 0  0  1  0  0 -1  1  0  0  0  1  1]
[ 0  1  0  0  1  1 -1  1  0  0  0  0]
[ 1  0  0  0  0  0  1 -1  1  0  0  1]
[ 0  1  1  1  0  0  0  1 -1  0  0  0]
[ 1  1  1  0  0  0  0  0  0 -1  0  1]
[ 1  1  0  1  0  1  0  0  0  0 -1  0]
[ 0  0  0  1  0  1  0  1  0  1  0 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1

3.C3⋊D4

    order := 24,
    length := 40,
    subgroup := MatrixGroup(9, Integer Ring) of order 2^3 * 3
    Generators:
        [ 3  1  1  2  1  1  0  0  0]
        [-1 -1  0 -1  0  0  0  0  0]
        [-1  0  0 -1 -1  0  0  0  0]
        [-2 -1 -1 -1 -1 -1  0  0  0]
        [-1  0 -1 -1  0  0  0  0  0]
        [-1  0  0 -1  0 -1  0  0  0]
        [ 0  0  0  0  0  0  1  0  0]
        [ 0  0  0  0  0  0  0  1  0]
        [ 0  0  0  0  0  0  0  0  1]

        [1 0 0 0 0 0 0 0 0]
        [0 0 1 0 0 0 0 0 0]
        [0 0 0 0 1 0 0 0 0]
        [0 0 0 1 0 0 0 0 0]
        [0 1 0 0 0 0 0 0 0]
        [0 0 0 0 0 1 0 0 0]
        [0 0 0 0 0 0 1 0 0]
        [0 0 0 0 0 0 0 1 0]
        [0 0 0 0 0 0 0 0 1]

        [ 2  1  1  0  1  0  0  0  0]
        [-1  0 -1  0 -1  0  0  0  0]
        [-1 -1  0  0 -1  0  0  0  0]
        [ 0  0  0  1  0  0  0  0  0]
        [-1 -1 -1  0  0  0  0  0  0]
        [ 0  0  0  0  0  1  0  0  0]
        [ 0  0  0  0  0  0  1  0  0]
        [ 0  0  0  0  0  0  0  1  0]
        [ 0  0  0  0  0  0  0  0  1]

        [ 2  1  1  0  1  0  0  0  0]
        [-1  0 -1  0 -1  0  0  0  0]
        [-1 -1  0  0 -1  0  0  0  0]
        [ 0  0  0  0  0  1  0  0  0]
        [-1 -1 -1  0  0  0  0  0  0]
        [ 0  0  0  1  0  0  0  0  0]
        [ 0  0  0  0  0  0  1  0  0]
        [ 0  0  0  0  0  0  0  1  0]
        [ 0  0  0  0  0  0  0  0  1]>

Orbit type:{4,12}

Orbit:
1
{@
    Mod: ( 2 -1 -1 -1 -1 -1  0  0  0),
    Mod: (0 0 0 0 0 1 0 0 0),
    Mod: ( 1  0  0 -1  0 -1  0  0  0),
    Mod: (0 0 0 1 0 0 0 0 0)
@}
Intersection Matrix:
[-1  1  0  1]
[ 1 -1  1  0]
[ 0  1 -1  1]
[ 1  0  1 -1]
Stabilizer Group Name:
C6
MatrixGroup(9, Integer Ring)
Generators:
    [1 0 0 0 0 0 0 0 0]
    [0 0 1 0 0 0 0 0 0]
    [0 0 0 0 1 0 0 0 0]
    [0 0 0 1 0 0 0 0 0]
    [0 1 0 0 0 0 0 0 0]
    [0 0 0 0 0 1 0 0 0]
    [0 0 0 0 0 0 1 0 0]
    [0 0 0 0 0 0 0 1 0]
    [0 0 0 0 0 0 0 0 1]

    [1 0 0 0 0 0 0 0 0]
    [0 1 0 0 0 0 0 0 0]
    [0 0 1 0 0 0 0 0 0]
    [0 0 0 0 0 1 0 0 0]
    [0 0 0 0 1 0 0 0 0]
    [0 0 0 1 0 0 0 0 0]
    [0 0 0 0 0 0 1 0 0]
    [0 0 0 0 0 0 0 1 0]
    [0 0 0 0 0 0 0 0 1]

2
{@
    Mod: ( 1  0  0  0 -1 -1  0  0  0),
    Mod: ( 1 -1  0  0  0 -1  0  0  0),
    Mod: ( 1 -1  0 -1  0  0  0  0  0),
    Mod: (0 0 1 0 0 0 0 0 0),
    Mod: ( 1  0 -1 -1  0  0  0  0  0),
    Mod: ( 1 -1  0  0 -1  0  0  0  0),
    Mod: ( 1  0  0 -1 -1  0  0  0  0),
    Mod: ( 1  0 -1  0  0 -1  0  0  0),
    Mod: ( 1  0 -1  0 -1  0  0  0  0),
    Mod: (0 1 0 0 0 0 0 0 0),
    Mod: (0 0 0 0 1 0 0 0 0),
    Mod: ( 1 -1 -1  0  0  0  0  0  0)
@}
Intersection Matrix:
[-1  0  1  0  1  0  0  0  0  0  1  1]
[ 0 -1  0  0  1  0  1  0  1  1  0  0]
[ 1  0 -1  0  0  0  0  1  1  1  0  0]
[ 0  0  0 -1  1  0  0  1  1  0  0  1]
[ 1  1  0  1 -1  1  0  0  0  0  0  0]
[ 0  0  0  0  1 -1  0  1  0  1  1  0]
[ 0  1  0  0  0  0 -1  1  0  0  1  1]
[ 0  0  1  1  0  1  1 -1  0  0  0  0]
[ 0  1  1  1  0  0  0  0 -1  0  1  0]
[ 0  1  1  0  0  1  0  0  0 -1  0  1]
[ 1  0  0  0  0  1  1  0  1  0 -1  0]
[ 1  0  0  1  0  0  1  0  0  1  0 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
    [ 2  1  1  0  1  0  0  0  0]
    [-1  0 -1  0 -1  0  0  0  0]
    [-1 -1  0  0 -1  0  0  0  0]
    [ 0  0  0  1  0  0  0  0  0]
    [-1 -1 -1  0  0  0  0  0  0]
    [ 0  0  0  0  0  1  0  0  0]
    [ 0  0  0  0  0  0  1  0  0]
    [ 0  0  0  0  0  0  0  1  0]
    [ 0  0  0  0  0  0  0  0  1]