Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
374 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 82 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. #10592410 | C2 | semidirect |
| 2. C3×#4717 | C2 | semidirect |
| 4. C3×#4466 | C2 | semidirect |
| 5. #10589137 | C2 | semidirect |
| 6. #10589128 | C2 | semidirect |
| 7. #10589124 | C2 | semidirect |
| 21. #63549 | C4 | semidirect |
| 22. #63546 | C4 | semidirect |
| 26. #4717 | D3 | semidirect |
| 37. #4466 | D3 | semidirect |
| 49. C3×Dic12 | C2×C4 | semidirect |
| 50. C3×D24 | C2×C4 | semidirect |
| 55. C3×C3⋊C16 | C2×C4 | semidirect |
| 140. Dic12 | C4×D3 | semidirect |
| 147. D24 | C4×D3 | semidirect |
| 154. C3⋊C16 | C4×D3 | semidirect |
| 268. C32 | AGL(1,ℤ/16) | semidirect |
| 306. C3 | #69091 | semidirect |
| 307. C3 | #70929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592410 | 2 |
| C3×#4717 | 2 |
| #10590634 | 2 |
| C3×#4466 | 2 |
| #10589137 | 2 |
| #10589128 | 2 |
| #10589124 | 2 |
| #70929 | 3 |
| #69091 | 3 |