Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
748 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 748 conjugacy classes of subgroups — too many to draw. Only its 171 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. C2×#19152034 | C2 | semidirect |
| 2. #26030733 | C2 | semidirect |
| 3. #26029104 | C2 | semidirect |
| 4. #26022305 | C2 | semidirect |
| 5. #26022285 | C2 | semidirect |
| 6. #26022010 | C2 | semidirect |
| 7. #26021968 | C2 | semidirect |
| 8. #26021960 | C2 | semidirect |
| 9. C22×D16×C89 | C2 | semidirect |
| 15. C2×#15667956 | C22 | semidirect |
| 16. C2×#15667953 | C22 | semidirect |
| 19. #19151981 | C22 | semidirect |
| 20. #19151973 | C22 | semidirect |
| 22. D8×Dic89 | C22 | semidirect |
| 26. #19151416 | C22 | semidirect |
| 27. #19151403 | C22 | semidirect |
| 28. #19151400 | C22 | semidirect |
| 29. #19151399 | C22 | semidirect |
| 70. C2×D8×C89 | D4 | semidirect |
| 183. C22×D16 | D89 | semidirect |
| 191. C89 | #33585 | semidirect |
| 233. C2×D8 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152034 | 2 |
| #26030733 | 2 |
| #26029104 | 2 |
| #26022305 | 2 |
| #26022285 | 2 |
| #26022010 | 2 |
| #26021968 | 2 |
| #26021960 | 2 |
| C22×D16×C89 | 2 |
| #33585 | 89 |