Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
381 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 381 conjugacy classes of subgroups — too many to draw. Only its 94 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. #10590763 | C2 | semidirect |
| 2. Dic3×D24 | C2 | semidirect |
| 4. #10589375 | C2 | semidirect |
| 5. C3×#4509 | C2 | semidirect |
| 6. C3×Dic3×C16 | C2 | semidirect |
| 7. #10589139 | C2 | semidirect |
| 21. #63546 | C4 | semidirect |
| 33. #4509 | D3 | semidirect |
| 35. Dic3×C16 | D3 | semidirect |
| 44. #3745 | C2×C4 | semidirect |
| 49. C3×D24 | C2×C4 | semidirect |
| 53. C3×C3⋊C16 | C2×C4 | semidirect |
| 139. D24 | C4×D3 | semidirect |
| 144. C3⋊C16 | C4×D3 | semidirect |
| 157. C3×Dic3 | D16 | semidirect |
| 263. Dic3 | D48 | semidirect |
| 264. C32 | C4×D16 | semidirect |
| 309. C3 | C4×D48 | semidirect |
| 310. C3 | #69174 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10590763 | 2 |
| Dic3×D24 | 2 |
| C2×#63546 | 2 |
| #10589375 | 2 |
| C3×#4509 | 2 |
| C3×Dic3×C16 | 2 |
| #10589139 | 2 |
| #69174 | 3 |
| C4×D48 | 3 |