Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
373 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 373 conjugacy classes of subgroups — too many to draw. Only its 96 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×C4×Dic12 | C2 | semidirect |
| 3. C2×#63547 | C2 | semidirect |
| 4. C4⋊(C3⋊(C3⋊C16)) | C2 | semidirect |
| 5. #10589114 | C2 | semidirect |
| 22. C4×Dic12 | D3 | semidirect |
| 40. C3×Dic12 | D4 | semidirect |
| 117. Dic12 | D12 | semidirect |
| 129. C32×C4 | SD32 | semidirect |
| 217. C3×C4 | #827 | semidirect |
| 218. C3×C4 | #828 | semidirect |
| 225. C32 | #2207 | semidirect |
| 259. C4 | #63547 | semidirect |
| 263. C3 | #70914 | semidirect |
| 264. C3 | #71294 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×Dic12 | 2 |
| C3×#4695 | 2 |
| C2×#63547 | 2 |
| C4⋊(C3⋊(C3⋊C16)) | 2 |
| #10589114 | 2 |
| #71294 | 3 |
| #70914 | 3 |