Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
668 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 668 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. #26033393 | C2 | semidirect |
| 2. #26032052 | C2 | semidirect |
| 3. #26022502 | C2 | semidirect |
| 4. #26022372 | C2 | semidirect |
| 5. #26022329 | C2 | semidirect |
| 6. #26022211 | C2 | semidirect |
| 7. #26022134 | C2 | semidirect |
| 8. C89×#2170 | C2 | semidirect |
| 9. #19152403 | C22 | semidirect |
| 12. #19152036 | C22 | semidirect |
| 16. C2×D1424 | C22 | semidirect |
| 17. C2×D1424 | C22 | semidirect |
| 18. #19151975 | C22 | semidirect |
| 20. #19151868 | C22 | semidirect |
| 22. #19151716 | C22 | semidirect |
| 23. #19151428 | C22 | semidirect |
| 24. #19151412 | C22 | semidirect |
| 25. #19151406 | C22 | semidirect |
| 26. #504×C89 | C22 | semidirect |
| 28. #364×C89 | C22 | semidirect |
| 29. #350×C89 | C22 | semidirect |
| 30. C4×C16×C89 | C22 | semidirect |
| 45. Dic712 | D4 | semidirect |
| 47. #15667957 | D4 | semidirect |
| 52. D1424 | D4 | semidirect |
| 150. #2170 | D89 | semidirect |
| 151. C89 | #33858 | semidirect |
| 161. #504 | C2×D89 | semidirect |
| 169. #364 | C2×D89 | semidirect |
| 172. #350 | C2×D89 | semidirect |
| 173. C4×C16 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033393 | 2 |
| #26032052 | 2 |
| #26022502 | 2 |
| #26022372 | 2 |
| #26022329 | 2 |
| #26022211 | 2 |
| #26022134 | 2 |
| C89×#2170 | 2 |
| #33858 | 89 |