Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
421 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 421 conjugacy classes of subgroups — too many to draw. Only its 80 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. #10592394 | C2 | semidirect |
| 2. C3×#4700 | C2 | semidirect |
| 3. #10590634 | C2 | semidirect |
| 4. C3×#4463 | C2 | semidirect |
| 5. #10589128 | C2 | semidirect |
| 22. #4700 | D3 | semidirect |
| 29. #4463 | D3 | semidirect |
| 41. C3×Dic12 | D4 | semidirect |
| 42. C3×D24 | D4 | semidirect |
| 118. Dic12 | D12 | semidirect |
| 131. D24 | D12 | semidirect |
| 239. C32 | #2213 | semidirect |
| 275. C3 | #69305 | semidirect |
| 276. C3 | #70926 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592394 | 2 |
| C3×#4700 | 2 |
| #10590634 | 2 |
| C3×#4463 | 2 |
| #10589128 | 2 |
| #70926 | 3 |
| #69305 | 3 |