Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
4512 conjugacy classes of subgroups; only the 881 normal subgroups are shown.
This group has 4512 conjugacy classes of subgroups — too many to draw. Only its 881 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×#3832 | C2 | semidirect |
| 2. C22×C32×Q16 | C2 | semidirect |
| 3. C22×#3755 | C2 | semidirect |
| 4. C2×#64128 | C2 | direct (N × H) |
| 5. C22×#3745 | C2 | semidirect |
| 6. C22×C8×C3⋊D3 | C2 | semidirect |
| 10. C2×#3832 | C22 | semidirect |
| 15. C2×C32×Q16 | C22 | semidirect |
| 17. C2×#3755 | C22 | semidirect |
| 19. #64128 | C22 | direct (N × H) |
| 20. C2×#3745 | C22 | semidirect |
| 21. C2×C8×C3⋊D3 | C22 | semidirect |
| 23. C22×C3×Q16 | D3 | semidirect |
| 36. #3832 | C23 | semidirect |
| 43. C32×Q16 | C23 | semidirect |
| 45. #3755 | C23 | semidirect |
| 47. #3745 | C23 | semidirect |
| 48. C8×C3⋊D3 | C23 | semidirect |
| 57. C2×C3×Q16 | C2×D3 | semidirect |
| 85. C22×Q16 | C3⋊D3 | semidirect |
| 104. C3×Q16 | C22×D3 | semidirect |
| 110. C22×C32 | #135 | semidirect |
| 128. C2×Q16 | C2×C3⋊D3 | semidirect |
| 153. C2×C32 | C2×#135 | semidirect |
| 172. Q16 | C22×C3⋊D3 | semidirect |
| 178. C22×C3 | #919 | semidirect |
| 188. C32 | C22×#135 | semidirect |
| 208. C2×C3 | C2×#919 | semidirect |
| 216. C22 | #64128 | direct (N × H) |
| 222. C3 | C22×#919 | semidirect |
| 225. C2 | C2×#64128 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3832 | 2 |
| C22×C32×Q16 | 2 |
| C22×#3755 | 2 |
| C2×#64128 | 2 |
| C22×#3745 | 2 |
| C22×C8×C3⋊D3 | 2 |
| C22×#919 | 3 |