Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
371 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 371 conjugacy classes of subgroups — too many to draw. Only its 72 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×#4895 | C2 | semidirect |
| 2. #10590880 | C2 | semidirect |
| 3. #10590634 | C2 | semidirect |
| 4. #10590630 | C2 | semidirect |
| 5. #10589361 | C2 | semidirect |
| 6. C3×#4495 | C2 | semidirect |
| 7. #10589134 | C2 | semidirect |
| 31. #4895 | D3 | semidirect |
| 38. #4495 | D3 | semidirect |
| 50. C3×Dic12 | D4 | semidirect |
| 53. C3×D24 | D4 | semidirect |
| 148. Dic12 | D12 | semidirect |
| 159. D24 | D12 | semidirect |
| 287. C32 | #2213 | semidirect |
| 330. C3 | #69263 | semidirect |
| 331. C3 | #70926 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4895 | 2 |
| #10590880 | 2 |
| #10590634 | 2 |
| #10590630 | 2 |
| #10589361 | 2 |
| C3×#4495 | 2 |
| #10589134 | 2 |
| #70926 | 3 |
| #69263 | 3 |