Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
393 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 393 conjugacy classes of subgroups — too many to draw. Only its 88 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×#63655 | C2 | semidirect |
| 2. C3×Dic3×Q16 | C2 | semidirect |
| 3. C2×C3×#828 | C2 | semidirect |
| 5. Dic3⋊(C3⋊C16) | C2 | semidirect |
| 6. #10589116 | C2 | semidirect |
| 7. #10589114 | C2 | semidirect |
| 25. Dic3×Q16 | D3 | semidirect |
| 29. C2×#828 | D3 | semidirect |
| 44. C32×Q16 | D4 | semidirect |
| 130. C3×Q16 | D12 | semidirect |
| 131. C3×Q16 | #67 | semidirect |
| 174. C3×Dic3 | SD32 | semidirect |
| 244. Q16 | #626 | semidirect |
| 290. Dic3 | #828 | semidirect |
| 291. C32 | #2207 | semidirect |
| 338. C3 | #70914 | semidirect |
| 339. C3 | #71475 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63655 | 2 |
| C3×Dic3×Q16 | 2 |
| C2×C3×#828 | 2 |
| #10590880 | 2 |
| Dic3⋊(C3⋊C16) | 2 |
| #10589116 | 2 |
| #10589114 | 2 |
| #71475 | 3 |
| #70914 | 3 |