Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
893 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 893 conjugacy classes of subgroups — too many to draw. Only its 152 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. #10596269 | C2 | semidirect |
| 3. C2×C3×#833 | C2 | semidirect |
| 4. #10591110 | C2 | semidirect |
| 5. #10589158 | C2 | semidirect |
| 14. C3×#940 | C4 | semidirect |
| 16. C3×#936 | C4 | semidirect |
| 28. C2×#833 | D3 | semidirect |
| 43. C2×C3×D12 | C2×C4 | semidirect |
| 45. C2×C3×Dic6 | C2×C4 | semidirect |
| 49. C4×C3⋊Dic3 | D4 | semidirect |
| 53. C3×C4×Dic3 | C2×C4 | semidirect |
| 73. #940 | Dic3 | semidirect |
| 75. #936 | Dic3 | semidirect |
| 148. C2×D12 | C2×Dic3 | semidirect |
| 150. C2×Dic6 | C2×Dic3 | semidirect |
| 173. C4×Dic3 | C2×Dic3 | semidirect |
| 336. C32 | #1911 | semidirect |
| 393. C3 | #70071 | semidirect |
| 394. C3 | #71853 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596269 | 2 |
| C3×#5805 | 2 |
| C2×C3×#833 | 2 |
| #10591110 | 2 |
| #10589158 | 2 |
| #71853 | 3 |
| #70071 | 3 |