Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
472 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 151 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. #26033393 | C2 | semidirect |
| 2. #26022565 | C2 | semidirect |
| 3. #26022564 | C2 | semidirect |
| 4. #26022559 | C2 | semidirect |
| 5. C2×#19151433 | C2 | semidirect |
| 6. #26022546 | C2 | semidirect |
| 7. C89×#3415 | C2 | semidirect |
| 10. #19152030 | C22 | semidirect |
| 11. C2×D1424 | C22 | semidirect |
| 12. #19151438 | C22 | semidirect |
| 13. #19151436 | C22 | semidirect |
| 14. #19151435 | C22 | semidirect |
| 15. #19151433 | C22 | semidirect |
| 16. #19151433 | C22 | semidirect |
| 17. #19151432 | C22 | semidirect |
| 18. C2×#15667918 | C22 | semidirect |
| 21. #508×C89 | C22 | semidirect |
| 22. C2×D16×C89 | C22 | semidirect |
| 98. #3415 | D89 | semidirect |
| 104. C89 | #33982 | semidirect |
| 110. #508 | C2×D89 | semidirect |
| 112. C2×D16 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033393 | 2 |
| #26022565 | 2 |
| #26022564 | 2 |
| #26022559 | 2 |
| C2×#19151433 | 2 |
| #26022546 | 2 |
| C89×#3415 | 2 |
| #33982 | 89 |