Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
565 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 565 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. C2×#63797 | C2 | semidirect |
| 2. C2×C3×D48 | C2 | semidirect |
| 3. #10590844 | C2 | semidirect |
| 4. C2×#63545 | C2 | semidirect |
| 5. #10589373 | C2 | semidirect |
| 6. C3×#4509 | C2 | semidirect |
| 7. #10589114 | C2 | semidirect |
| 14. C2×C3×D24 | C22 | semidirect |
| 19. C2×C32×C16 | C22 | semidirect |
| 20. C2×C3⋊(C3⋊C16) | C22 | semidirect |
| 21. C3×#818 | C22 | semidirect |
| 31. C2×D48 | D3 | semidirect |
| 35. #4509 | D3 | semidirect |
| 58. C3×D24 | D4 | semidirect |
| 59. C3×D24 | D4 | semidirect |
| 79. C2×D24 | C2×D3 | semidirect |
| 86. C2×C3×C16 | C2×D3 | semidirect |
| 87. C2×C3×C16 | C2×D3 | semidirect |
| 92. #818 | C2×D3 | semidirect |
| 169. D24 | D12 | semidirect |
| 170. D24 | #67 | semidirect |
| 186. C2×C3⋊D3 | D16 | semidirect |
| 213. C2×C16 | D32 | semidirect |
| 344. C32 | #2184 | semidirect |
| 405. C3 | #69191 | semidirect |
| 406. C3 | #71467 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63797 | 2 |
| C2×C3×D48 | 2 |
| #10590844 | 2 |
| C2×#63545 | 2 |
| #10589373 | 2 |
| C3×#4509 | 2 |
| #10589114 | 2 |
| #71467 | 3 |
| #69191 | 3 |