Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
512 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 512 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. #26030912 | C2 | semidirect |
| 3. #26022473 | C2 | semidirect |
| 4. #26022425 | C2 | semidirect |
| 5. #26022334 | C2 | semidirect |
| 6. #26022333 | C2 | semidirect |
| 8. #26022142 | C2 | semidirect |
| 9. #26022140 | C2 | semidirect |
| 10. #26022067 | C2 | semidirect |
| 11. C89×#2231 | C2 | semidirect |
| 17. #19151978 | C22 | semidirect |
| 26. #19151704 | C22 | semidirect |
| 31. #19151420 | C22 | semidirect |
| 32. #19151419 | C22 | semidirect |
| 33. #19151415 | C22 | semidirect |
| 34. #19151413 | C22 | semidirect |
| 37. #19151375 | C22 | semidirect |
| 38. #499×C89 | C22 | semidirect |
| 40. #365×C89 | C22 | semidirect |
| 41. #364×C89 | C22 | semidirect |
| 211. #2231 | D89 | semidirect |
| 218. C89 | #33693 | semidirect |
| 224. #499 | C2×D89 | semidirect |
| 241. #365 | C2×D89 | semidirect |
| 243. #364 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030912 | 2 |
| #26029150 | 2 |
| #26022473 | 2 |
| #26022425 | 2 |
| #26022334 | 2 |
| #26022333 | 2 |
| #26022204 | 2 |
| #26022142 | 2 |
| #26022140 | 2 |
| #26022067 | 2 |
| C89×#2231 | 2 |
| #33693 | 89 |