Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
668 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 135 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. #26033389 | C2 | semidirect |
| 2. #26032051 | C2 | semidirect |
| 3. #26022369 | C2 | semidirect |
| 4. #26022325 | C2 | semidirect |
| 5. #26022208 | C2 | semidirect |
| 6. #26022134 | C2 | semidirect |
| 7. #26022090 | C2 | semidirect |
| 8. C89×#2246 | C2 | semidirect |
| 10. #19152399 | C22 | semidirect |
| 11. #19152034 | C22 | semidirect |
| 16. #19152014 | C22 | semidirect |
| 18. #19151865 | C22 | semidirect |
| 21. #19151716 | C22 | semidirect |
| 22. #19151428 | C22 | semidirect |
| 23. #19151419 | C22 | semidirect |
| 24. #19151411 | C22 | semidirect |
| 25. #19151406 | C22 | semidirect |
| 26. #19151381 | C22 | semidirect |
| 27. C2×D16×C89 | C22 | semidirect |
| 28. C2×D16×C89 | C22 | semidirect |
| 29. #493×C89 | C22 | semidirect |
| 30. C4×C16×C89 | C22 | semidirect |
| 44. Dic712 | D4 | semidirect |
| 45. #15667957 | D4 | semidirect |
| 47. D1424 | D4 | semidirect |
| 145. #2246 | D89 | semidirect |
| 151. C89 | #33858 | semidirect |
| 159. C2×D16 | C2×D89 | semidirect |
| 160. C2×D16 | C2×D89 | semidirect |
| 162. #493 | C2×D89 | semidirect |
| 173. C4×C16 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033389 | 2 |
| #26032051 | 2 |
| #26022369 | 2 |
| #26022325 | 2 |
| #26022208 | 2 |
| #26022134 | 2 |
| #26022090 | 2 |
| C89×#2246 | 2 |
| #33858 | 89 |