Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
564 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 131 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. #26029163 | C2 | semidirect |
| 2. #26022464 | C2 | semidirect |
| 3. #26022420 | C2 | semidirect |
| 4. #26022325 | C2 | semidirect |
| 5. #26022197 | C2 | semidirect |
| 6. #26022148 | C2 | semidirect |
| 7. #26022064 | C2 | semidirect |
| 8. C89×#3184 | C2 | semidirect |
| 18. #19151420 | C22 | semidirect |
| 19. #19151419 | C22 | semidirect |
| 20. #19151411 | C22 | semidirect |
| 23. #19151376 | C22 | semidirect |
| 25. #498×C89 | C22 | semidirect |
| 26. #493×C89 | C22 | semidirect |
| 31. #442×C89 | C22 | semidirect |
| 80. Dic356 | #41 | semidirect |
| 84. D712 | #41 | semidirect |
| 170. #3184 | D89 | semidirect |
| 178. C89 | #33688 | semidirect |
| 183. #498 | C2×D89 | semidirect |
| 184. #493 | C2×D89 | semidirect |
| 193. #442 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029163 | 2 |
| #26022464 | 2 |
| #26022420 | 2 |
| #26022325 | 2 |
| #26022197 | 2 |
| #26022148 | 2 |
| #26022064 | 2 |
| C89×#3184 | 2 |
| #33688 | 89 |