Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
564 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26029162 | C2 | semidirect |
| 3. #26022467 | C2 | semidirect |
| 4. #26022464 | C2 | semidirect |
| 5. #26022421 | C2 | semidirect |
| 6. #26022326 | C2 | semidirect |
| 7. #26022198 | C2 | semidirect |
| 8. #26022151 | C2 | semidirect |
| 9. #26022147 | C2 | semidirect |
| 10. #26022061 | C2 | semidirect |
| 11. C89×#2190 | C2 | semidirect |
| 15. #19151995 | C22 | semidirect |
| 16. #19151973 | C22 | semidirect |
| 24. #19151710 | C22 | semidirect |
| 25. #19151709 | C22 | semidirect |
| 30. #19151421 | C22 | semidirect |
| 31. #19151420 | C22 | semidirect |
| 32. #19151418 | C22 | semidirect |
| 33. #19151412 | C22 | semidirect |
| 34. #19151411 | C22 | semidirect |
| 37. #19151375 | C22 | semidirect |
| 132. Q16×C89 | #41 | semidirect |
| 137. D8×C89 | #41 | semidirect |
| 215. #2190 | D89 | semidirect |
| 219. C89 | #33688 | semidirect |
| 319. Q16 | #13083573 | semidirect |
| 326. D8 | #13083573 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030985 | 2 |
| #26029162 | 2 |
| #26022467 | 2 |
| #26022464 | 2 |
| #26022421 | 2 |
| #26022326 | 2 |
| #26022198 | 2 |
| #26022151 | 2 |
| #26022147 | 2 |
| #26022061 | 2 |
| C89×#2190 | 2 |
| #33688 | 89 |