Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
322 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 4. #26018428 | C2 | semidirect |
| 5. #26018427 | C2 | semidirect |
| 6. #26018426 | C2 | semidirect |
| 7. C89×#1414 | C2 | semidirect |
| 9. #125×D89 | C4 | semidirect |
| 12. #19151955 | C4 | semidirect |
| 13. #19151953 | C4 | semidirect |
| 19. C4×#13083557 | C4 | semidirect |
| 165. #1414 | D89 | semidirect |
| 166. C89 | #13604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030649 | 2 |
| #26021934 | 2 |
| #26021916 | 2 |
| #26018428 | 2 |
| #26018427 | 2 |
| #26018426 | 2 |
| C89×#1414 | 2 |
| #13604 | 89 |