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.
| subgroup | G/H | |
|---|---|---|
| center | C23 | D4×D9 |
| commutator, cosocle | C4×C9 | C25 |
| Frattini | C3×C4 | C24×D3 |
| Fitting | C22×C9×D8 | C2 |
| socle | C23×C3 | D3×D4 |
| hypercenter | C22×D8 | D9 |
| hypocenter | C9 | C22×#135 |
| LCS | G ▷ C4×C9 ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ C22×D8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#3699 | C2 | semidirect |
| 2. C22×C9×D8 | C2 | semidirect |
| 3. C22×#3672 | C2 | semidirect |
| 4. C2×#63474 | C2 | direct (N × H) |
| 5. C22×C8×D9 | C2 | semidirect |
| 6. C22×Dic36 | C2 | semidirect |
| 12. C2×#3699 | C22 | semidirect |
| 15. C2×C9×D8 | C22 | semidirect |
| 17. C2×#3672 | C22 | semidirect |
| 19. #63474 | C22 | direct (N × H) |
| 20. C2×C8×D9 | C22 | semidirect |
| 21. C2×Dic36 | C22 | semidirect |
| 38. #3699 | C23 | semidirect |
| 43. C9×D8 | C23 | semidirect |
| 45. #3672 | C23 | semidirect |
| 47. C8×D9 | C23 | semidirect |
| 48. Dic36 | C23 | semidirect |
| 87. C22×D8 | D9 | semidirect |
| 112. C22×C9 | #135 | semidirect |
| 130. C2×D8 | C2×D9 | semidirect |
| 154. C2×C9 | C2×#135 | semidirect |
| 174. D8 | C22×D9 | semidirect |
| 188. C9 | C22×#135 | semidirect |
| 216. C22 | #63474 | direct (N × H) |
| 225. C2 | C2×#63474 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3699 | 2 |
| C22×C9×D8 | 2 |
| C22×#3672 | 2 |
| C2×#63474 | 2 |
| C22×C8×D9 | 2 |
| C22×Dic36 | 2 |
| C22×#912 | 3 |