Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
590 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 151 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. #499×D89 | C2 | semidirect |
| 3. #26022499 | C2 | semidirect |
| 4. #26022498 | C2 | semidirect |
| 5. #26022493 | C2 | semidirect |
| 6. #26022482 | C2 | semidirect |
| 7. #26021961 | C2 | semidirect |
| 8. #26021845 | C2 | semidirect |
| 9. C89×#2244 | C2 | semidirect |
| 154. #2244 | D89 | semidirect |
| 158. C89 | #33708 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #499×D89 | 2 |
| #26030679 | 2 |
| #26022499 | 2 |
| #26022498 | 2 |
| #26022493 | 2 |
| #26022482 | 2 |
| #26021961 | 2 |
| #26021845 | 2 |
| C89×#2244 | 2 |
| #33708 | 89 |