Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
372 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 65 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. #26022491 | C2 | semidirect |
| 3. #26019762 | C2 | semidirect |
| 4. #26018296 | C2 | semidirect |
| 5. #26018219 | C2 | semidirect |
| 6. #26018209 | C2 | semidirect |
| 7. C89×#2226 | C2 | semidirect |
| 19. #19151374 | C22 | semidirect |
| 20. #19151349 | C22 | semidirect |
| 22. #500×C89 | C22 | semidirect |
| 25. C4⋊C16×C89 | C22 | semidirect |
| 98. D8×C89 | SD16 | semidirect |
| 169. #2226 | D89 | semidirect |
| 174. C89 | #12378 | semidirect |
| 177. #500 | C2×D89 | semidirect |
| 187. C4⋊C16 | C2×D89 | semidirect |
| 253. D8 | #13083561 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031862 | 2 |
| #26022491 | 2 |
| #26019762 | 2 |
| #26018296 | 2 |
| #26018219 | 2 |
| #26018209 | 2 |
| C89×#2226 | 2 |
| #12378 | 89 |