Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
464 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 2. #26022531 | C2 | semidirect |
| 3. #26022459 | C2 | semidirect |
| 4. #26022453 | C2 | semidirect |
| 5. #26022416 | C2 | semidirect |
| 6. #26022357 | C2 | semidirect |
| 8. #26022037 | C2 | semidirect |
| 9. C4×Q32×C89 | C2 | semidirect |
| 139. C4×Q32 | D89 | semidirect |
| 142. C89 | #33919 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26032622 | 2 |
| #26022531 | 2 |
| #26022459 | 2 |
| #26022453 | 2 |
| #26022416 | 2 |
| #26022357 | 2 |
| #26022085 | 2 |
| #26022037 | 2 |
| C4×Q32×C89 | 2 |
| #33919 | 89 |