Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
564 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 135 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. #26030990 | C2 | semidirect |
| 2. #26022466 | C2 | semidirect |
| 3. #26022423 | C2 | semidirect |
| 4. #26022328 | C2 | semidirect |
| 5. #26022198 | C2 | semidirect |
| 6. #26022150 | C2 | semidirect |
| 7. #26022064 | C2 | semidirect |
| 8. C89×#2956 | C2 | semidirect |
| 11. #19151996 | C22 | semidirect |
| 12. #19151975 | C22 | semidirect |
| 17. #19151711 | C22 | semidirect |
| 18. #19151422 | C22 | semidirect |
| 19. #19151419 | C22 | semidirect |
| 20. #19151410 | C22 | semidirect |
| 23. #19151376 | C22 | semidirect |
| 96. Q16×C89 | #41 | semidirect |
| 100. D8×C89 | #41 | semidirect |
| 171. #2956 | D89 | semidirect |
| 178. C89 | #33688 | semidirect |
| 259. Q16 | #13083574 | semidirect |
| 265. D8 | #13083574 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030990 | 2 |
| #26022466 | 2 |
| #26022423 | 2 |
| #26022328 | 2 |
| #26022198 | 2 |
| #26022150 | 2 |
| #26022064 | 2 |
| C89×#2956 | 2 |
| #33688 | 89 |