Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
578 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 3. #26022499 | C2 | semidirect |
| 4. #26022498 | C2 | semidirect |
| 5. #26022497 | C2 | semidirect |
| 6. #26022478 | C2 | semidirect |
| 9. C89×#2245 | C2 | semidirect |
| 151. #2245 | D89 | semidirect |
| 155. C89 | #33705 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030765 | 2 |
| #494×D89 | 2 |
| #26022499 | 2 |
| #26022498 | 2 |
| #26022497 | 2 |
| #26022478 | 2 |
| #26021970 | 2 |
| #26021845 | 2 |
| C89×#2245 | 2 |
| #33705 | 89 |