Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
712 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 712 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×#19152039 | C2 | semidirect |
| 3. #26029120 | C2 | semidirect |
| 4. #26022312 | C2 | semidirect |
| 5. #26022290 | C2 | semidirect |
| 6. #26022010 | C2 | semidirect |
| 7. #26021968 | C2 | semidirect |
| 8. #26021960 | C2 | semidirect |
| 9. C22×SD32×C89 | C2 | semidirect |
| 15. C2×#15667958 | C22 | semidirect |
| 16. C2×#15667955 | C22 | semidirect |
| 22. Q16×Dic89 | C22 | semidirect |
| 26. #19151416 | C22 | semidirect |
| 27. #19151403 | C22 | semidirect |
| 28. #19151400 | C22 | semidirect |
| 67. C2×Q16×C89 | D4 | semidirect |
| 178. C22×SD32 | D89 | semidirect |
| 186. C89 | #33587 | semidirect |
| 221. C2×Q16 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152039 | 2 |
| #26030733 | 2 |
| #26029120 | 2 |
| #26022312 | 2 |
| #26022290 | 2 |
| #26022010 | 2 |
| #26021968 | 2 |
| #26021960 | 2 |
| C22×SD32×C89 | 2 |
| #33587 | 89 |