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. #26030908 | C2 | semidirect |
| 3. #26022470 | C2 | semidirect |
| 4. #26022429 | C2 | semidirect |
| 5. #26022428 | C2 | semidirect |
| 6. #26022330 | C2 | semidirect |
| 8. #26022146 | C2 | semidirect |
| 9. #26022144 | C2 | semidirect |
| 10. #26022067 | C2 | semidirect |
| 11. C89×#2214 | C2 | semidirect |
| 16. #19152000 | C22 | semidirect |
| 25. #19151705 | C22 | semidirect |
| 30. #19151422 | C22 | semidirect |
| 31. #19151421 | C22 | semidirect |
| 32. #19151419 | C22 | semidirect |
| 33. #19151414 | C22 | semidirect |
| 37. #19151375 | C22 | semidirect |
| 39. #494×C89 | C22 | semidirect |
| 41. #364×C89 | C22 | semidirect |
| 42. #362×C89 | C22 | semidirect |
| 213. #2214 | D89 | semidirect |
| 218. C89 | #33693 | semidirect |
| 225. #494 | C2×D89 | semidirect |
| 243. #364 | C2×D89 | semidirect |
| 245. #362 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030908 | 2 |
| #26029150 | 2 |
| #26022470 | 2 |
| #26022429 | 2 |
| #26022428 | 2 |
| #26022330 | 2 |
| #26022201 | 2 |
| #26022146 | 2 |
| #26022144 | 2 |
| #26022067 | 2 |
| C89×#2214 | 2 |
| #33693 | 89 |