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. #26030899 | C2 | semidirect |
| 2. #26029150 | C2 | semidirect |
| 3. #26022465 | C2 | semidirect |
| 4. #26022429 | C2 | semidirect |
| 5. #26022428 | C2 | semidirect |
| 6. #26022325 | C2 | semidirect |
| 7. #26022196 | C2 | semidirect |
| 8. #26022153 | C2 | semidirect |
| 9. #26022151 | C2 | semidirect |
| 10. #26022067 | C2 | semidirect |
| 11. C89×#2213 | C2 | semidirect |
| 16. #19152000 | C22 | semidirect |
| 25. #19151710 | C22 | semidirect |
| 30. #19151422 | C22 | semidirect |
| 31. #19151421 | C22 | semidirect |
| 32. #19151419 | C22 | semidirect |
| 33. #19151411 | C22 | semidirect |
| 37. #19151375 | C22 | semidirect |
| 39. #493×C89 | C22 | semidirect |
| 41. #364×C89 | C22 | semidirect |
| 42. #361×C89 | C22 | semidirect |
| 219. #2213 | D89 | semidirect |
| 224. C89 | #33692 | semidirect |
| 231. #493 | C2×D89 | semidirect |
| 249. #364 | C2×D89 | semidirect |
| 251. #361 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030899 | 2 |
| #26029150 | 2 |
| #26022465 | 2 |
| #26022429 | 2 |
| #26022428 | 2 |
| #26022325 | 2 |
| #26022196 | 2 |
| #26022153 | 2 |
| #26022151 | 2 |
| #26022067 | 2 |
| C89×#2213 | 2 |
| #33692 | 89 |