Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
668 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 143 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. #26033390 | C2 | semidirect |
| 2. #26032052 | C2 | semidirect |
| 3. #26022502 | C2 | semidirect |
| 4. #26022373 | C2 | semidirect |
| 5. #26022328 | C2 | semidirect |
| 6. #26022210 | C2 | semidirect |
| 7. #26022090 | C2 | semidirect |
| 8. C89×#2178 | C2 | semidirect |
| 10. #19152400 | C22 | semidirect |
| 12. #19152033 | C22 | semidirect |
| 14. C2×D1424 | C22 | semidirect |
| 15. C2×D1424 | C22 | semidirect |
| 17. #19152014 | C22 | semidirect |
| 18. #19151975 | C22 | semidirect |
| 19. #19151869 | C22 | semidirect |
| 23. #19151419 | C22 | semidirect |
| 24. #19151410 | C22 | semidirect |
| 25. #19151381 | C22 | semidirect |
| 27. #443×C89 | C22 | semidirect |
| 28. #368×C89 | C22 | semidirect |
| 29. #359×C89 | C22 | semidirect |
| 30. C4×C16×C89 | C22 | semidirect |
| 58. Q32×C89 | D4 | semidirect |
| 59. SD32×C89 | D4 | semidirect |
| 60. D16×C89 | D4 | semidirect |
| 149. #2178 | D89 | semidirect |
| 151. C89 | #33858 | semidirect |
| 167. #443 | C2×D89 | semidirect |
| 168. #368 | C2×D89 | semidirect |
| 171. #359 | C2×D89 | semidirect |
| 173. C4×C16 | C2×D89 | semidirect |
| 190. Q32 | D356 | semidirect |
| 192. SD32 | D356 | semidirect |
| 197. D16 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033390 | 2 |
| #26032052 | 2 |
| #26022502 | 2 |
| #26022373 | 2 |
| #26022328 | 2 |
| #26022210 | 2 |
| #26022090 | 2 |
| C89×#2178 | 2 |
| #33858 | 89 |