Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
564 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 121 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. #26030985 | C2 | semidirect |
| 2. #26029161 | C2 | semidirect |
| 3. #26022466 | C2 | semidirect |
| 4. #26022422 | C2 | semidirect |
| 5. #26022327 | C2 | semidirect |
| 6. #26022200 | C2 | semidirect |
| 7. #26022197 | C2 | semidirect |
| 8. #26022153 | C2 | semidirect |
| 9. #26022149 | C2 | semidirect |
| 10. #26022061 | C2 | semidirect |
| 11. C89×#2238 | C2 | semidirect |
| 17. #19151995 | C22 | semidirect |
| 18. #19151973 | C22 | semidirect |
| 26. #19151710 | C22 | semidirect |
| 27. #19151709 | C22 | semidirect |
| 31. #19151422 | C22 | semidirect |
| 32. #19151418 | C22 | semidirect |
| 33. #19151410 | C22 | semidirect |
| 37. #19151375 | C22 | semidirect |
| 40. #365×C89 | C22 | semidirect |
| 41. #361×C89 | C22 | semidirect |
| 108. Dic356 | #41 | semidirect |
| 113. D712 | #41 | semidirect |
| 211. #2238 | D89 | semidirect |
| 219. C89 | #33688 | semidirect |
| 242. #365 | C2×D89 | semidirect |
| 245. #361 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030985 | 2 |
| #26029161 | 2 |
| #26022466 | 2 |
| #26022422 | 2 |
| #26022327 | 2 |
| #26022200 | 2 |
| #26022197 | 2 |
| #26022153 | 2 |
| #26022149 | 2 |
| #26022061 | 2 |
| C89×#2238 | 2 |
| #33688 | 89 |