Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
393 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 393 conjugacy classes of subgroups — too many to draw. Only its 102 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×C32×SD32 | C2 | semidirect |
| 2. C3×Dic3×Q16 | C2 | semidirect |
| 3. C2×C3×#828 | C2 | semidirect |
| 5. C3×#4562 | C2 | semidirect |
| 6. C3×#4509 | C2 | semidirect |
| 7. C3×Dic3⋊C16 | C2 | semidirect |
| 9. #71475 | C3 | direct (N × H) |
| 25. C2×C3×SD32 | D3 | semidirect |
| 26. C2×C3×SD32 | C2×C3 | semidirect |
| 29. Dic3×Q16 | C2×C3 | semidirect |
| 30. C2×#828 | C2×C3 | semidirect |
| 35. #4562 | C2×C3 | semidirect |
| 36. #4509 | C2×C3 | semidirect |
| 37. Dic3⋊C16 | C2×C3 | semidirect |
| 44. C32×Q16 | D4 | semidirect |
| 108. C2×SD32 | C3×D3 | semidirect |
| 130. C3×Q16 | #67 | semidirect |
| 131. C3×Q16 | C3×D4 | semidirect |
| 174. C3×Dic3 | SD32 | semidirect |
| 244. Q16 | C3×#67 | semidirect |
| 290. Dic3 | C3×SD32 | semidirect |
| 291. C32 | #2207 | semidirect |
| 338. C3 | #71475 | direct (N × H) |
| 339. C3 | C3×#2207 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×SD32 | 2 |
| C3×Dic3×Q16 | 2 |
| C2×C3×#828 | 2 |
| C3×#5151 | 2 |
| C3×#4562 | 2 |
| C3×#4509 | 2 |
| C3×Dic3⋊C16 | 2 |
| C3×#2207 | 3 |
| #71475 | 3 |