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. #26030765 | C2 | semidirect |
| 3. #26022497 | C2 | semidirect |
| 4. #26022495 | C2 | semidirect |
| 5. #26022494 | C2 | semidirect |
| 6. #26022490 | C2 | semidirect |
| 7. #26021958 | C2 | semidirect |
| 8. #346×D89 | C2 | semidirect |
| 9. C89×#2245 | C2 | semidirect |
| 152. #2245 | D89 | semidirect |
| 158. C89 | #33701 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030765 | 2 |
| #26030681 | 2 |
| #26022497 | 2 |
| #26022495 | 2 |
| #26022494 | 2 |
| #26022490 | 2 |
| #26021958 | 2 |
| #346×D89 | 2 |
| C89×#2245 | 2 |
| #33701 | 89 |