Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
482 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26022903 | C2 | semidirect |
| 5. #26018146 | C2 | semidirect |
| 6. #26018107 | C2 | semidirect |
| 7. C89×#1491 | C2 | semidirect |
| 10. #19151893 | C4 | semidirect |
| 11. #19151798 | C4 | semidirect |
| 185. #1491 | D89 | semidirect |
| 188. C89 | #9330 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030374 | 2 |
| #26022903 | 2 |
| #26021171 | 2 |
| #26018761 | 2 |
| #26018146 | 2 |
| #26018107 | 2 |
| C89×#1491 | 2 |
| #9330 | 89 |