Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
888 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 888 conjugacy classes of subgroups — too many to draw. Only its 214 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×C9×Q16 | C2 | semidirect |
| 2. C2×#63509 | C2 | semidirect |
| 3. C22×#3675 | C2 | semidirect |
| 5. #10588871 | C2 | direct (N × H) |
| 6. C2×C8×Dic9 | C2 | semidirect |
| 11. C2×C9×Q16 | C22 | semidirect |
| 14. #63509 | C22 | semidirect |
| 16. C2×#3675 | C22 | semidirect |
| 22. C8×Dic9 | C22 | semidirect |
| 87. C22×Q16 | D9 | semidirect |
| 129. C2×Q16 | C2×D9 | semidirect |
| 161. C2×C9 | #495 | semidirect |
| 198. C9 | C2×#495 | semidirect |
| 236. C2 | #10588871 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C9×Q16 | 2 |
| C2×#63509 | 2 |
| C22×#3675 | 2 |
| C22×D72 | 2 |
| #10588871 | 2 |
| C2×C8×Dic9 | 2 |
| C2×#5191 | 3 |