Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
624 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C33×D4 | C2 | semidirect |
| 2. C3×#3828 | C2 | semidirect |
| 3. C3×#3754 | C2 | semidirect |
| 4. C3×#3753 | C2 | semidirect |
| 5. C3×#3748 | C2 | semidirect |
| 6. #64141 | C3 | direct (N × H) |
| 13. C3×C4⋊(C3⋊D3) | C22 | semidirect |
| 15. C3×#634 | C22 | semidirect |
| 16. C3×C3⋊(C3⋊C8) | C22 | semidirect |
| 18. C2×C32×D4 | D3 | semidirect |
| 19. C2×C32×D4 | C2×C3 | semidirect |
| 20. #3828 | C2×C3 | semidirect |
| 22. #3754 | C2×C3 | semidirect |
| 23. #3753 | C2×C3 | semidirect |
| 24. #3748 | C2×C3 | semidirect |
| 50. C4⋊(C3⋊D3) | C22×C3 | semidirect |
| 52. #634 | C22×C3 | semidirect |
| 57. C3⋊(C3⋊C8) | C22×C3 | semidirect |
| 65. C2×C3×D4 | C3×D3 | semidirect |
| 66. C2×C3×D4 | C3⋊D3 | semidirect |
| 94. C33 | AGL(1,ℤ/8) | semidirect |
| 129. C2×D4 | C3×C3⋊D3 | semidirect |
| 153. C32 | #932 | semidirect |
| 154. C32 | C3×AGL(1,ℤ/8) | semidirect |
| 183. C3 | C3×#932 | semidirect |
| 184. C3 | #64141 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×D4 | 2 |
| C3×#3828 | 2 |
| C3×#3754 | 2 |
| C3×#3753 | 2 |
| C3×#3748 | 2 |
| #64141 | 3 |
| C3×#932 | 3 |