Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
405 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 405 conjugacy classes of subgroups — too many to draw. Only its 84 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. C3×#4872 | C2 | semidirect |
| 2. #10590880 | C2 | semidirect |
| 3. C2×#63546 | C2 | semidirect |
| 4. C2×#63545 | C2 | semidirect |
| 5. #10589357 | C2 | semidirect |
| 6. C3×#4491 | C2 | semidirect |
| 7. Dic3⋊(C3⋊C16) | C2 | semidirect |
| 29. #4872 | D3 | semidirect |
| 36. #4491 | D3 | semidirect |
| 54. C3×D24 | D4 | semidirect |
| 154. D24 | D12 | semidirect |
| 174. C3×Dic3 | D16 | semidirect |
| 295. Dic3 | #826 | semidirect |
| 296. C32 | #2206 | semidirect |
| 348. C3 | #69202 | semidirect |
| 349. C3 | #70889 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4872 | 2 |
| #10590880 | 2 |
| C2×#63546 | 2 |
| C2×#63545 | 2 |
| #10589357 | 2 |
| C3×#4491 | 2 |
| Dic3⋊(C3⋊C16) | 2 |
| #70889 | 3 |
| #69202 | 3 |