Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2256 conjugacy classes of subgroups; only the 614 normal subgroups are shown.
This group has 2256 conjugacy classes of subgroups — too many to draw. Only its 614 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. C22×#3701 | C2 | semidirect |
| 2. C22×C9×Q16 | C2 | semidirect |
| 3. C22×#3675 | C2 | semidirect |
| 4. C2×#63481 | C2 | direct (N × H) |
| 5. C22×D72 | C2 | semidirect |
| 6. C22×C8×D9 | C2 | semidirect |
| 10. C2×#3701 | C22 | semidirect |
| 15. C2×C9×Q16 | C22 | semidirect |
| 17. C2×#3675 | C22 | semidirect |
| 19. #63481 | C22 | direct (N × H) |
| 20. C2×D72 | C22 | semidirect |
| 21. C2×C8×D9 | C22 | semidirect |
| 36. #3701 | C23 | semidirect |
| 43. C9×Q16 | C23 | semidirect |
| 45. #3675 | C23 | semidirect |
| 47. D72 | C23 | semidirect |
| 48. C8×D9 | C23 | semidirect |
| 85. C22×Q16 | D9 | semidirect |
| 110. C22×C9 | #135 | semidirect |
| 128. C2×Q16 | C2×D9 | semidirect |
| 153. C2×C9 | C2×#135 | semidirect |
| 172. Q16 | C22×D9 | semidirect |
| 188. C9 | C22×#135 | semidirect |
| 216. C22 | #63481 | direct (N × H) |
| 225. C2 | C2×#63481 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3701 | 2 |
| C22×C9×Q16 | 2 |
| C22×#3675 | 2 |
| C2×#63481 | 2 |
| C22×D72 | 2 |
| C22×C8×D9 | 2 |
| C22×#919 | 3 |