Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
536 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 123 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. #26030903 | C2 | semidirect |
| 2. #26029150 | C2 | semidirect |
| 3. #26022468 | C2 | semidirect |
| 4. #26022425 | C2 | semidirect |
| 5. #26022329 | C2 | semidirect |
| 6. #26022328 | C2 | semidirect |
| 7. #26022199 | C2 | semidirect |
| 8. #26022149 | C2 | semidirect |
| 9. #26022147 | C2 | semidirect |
| 10. #26022067 | C2 | semidirect |
| 11. C89×#2231 | C2 | semidirect |
| 17. #19151975 | C22 | semidirect |
| 26. #19151709 | C22 | semidirect |
| 31. #19151420 | C22 | semidirect |
| 32. #19151419 | C22 | semidirect |
| 33. #19151412 | C22 | semidirect |
| 34. #19151410 | C22 | semidirect |
| 37. #19151375 | C22 | semidirect |
| 38. #499×C89 | C22 | semidirect |
| 40. #365×C89 | C22 | semidirect |
| 41. #364×C89 | C22 | semidirect |
| 217. #2231 | D89 | semidirect |
| 224. C89 | #33692 | semidirect |
| 230. #499 | C2×D89 | semidirect |
| 247. #365 | C2×D89 | semidirect |
| 249. #364 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030903 | 2 |
| #26029150 | 2 |
| #26022468 | 2 |
| #26022425 | 2 |
| #26022329 | 2 |
| #26022328 | 2 |
| #26022199 | 2 |
| #26022149 | 2 |
| #26022147 | 2 |
| #26022067 | 2 |
| C89×#2231 | 2 |
| #33692 | 89 |