Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
512 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 512 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 |
|---|---|---|
| 2. #26022469 | C2 | semidirect |
| 3. #26022425 | C2 | semidirect |
| 4. #26022330 | C2 | semidirect |
| 6. #26022141 | C2 | semidirect |
| 7. #26022068 | C2 | semidirect |
| 8. C89×#3177 | C2 | semidirect |
| 18. #19151420 | C22 | semidirect |
| 19. #19151419 | C22 | semidirect |
| 20. #19151414 | C22 | semidirect |
| 23. #19151376 | C22 | semidirect |
| 25. #499×C89 | C22 | semidirect |
| 26. #494×C89 | C22 | semidirect |
| 30. #441×C89 | C22 | semidirect |
| 161. #3177 | D89 | semidirect |
| 169. C89 | #33693 | semidirect |
| 174. #499 | C2×D89 | semidirect |
| 175. #494 | C2×D89 | semidirect |
| 183. #441 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029156 | 2 |
| #26022469 | 2 |
| #26022425 | 2 |
| #26022330 | 2 |
| #26022202 | 2 |
| #26022141 | 2 |
| #26022068 | 2 |
| C89×#3177 | 2 |
| #33693 | 89 |