Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
302 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 81 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. M64×D89 | C2 | semidirect |
| 3. #367×D89 | C2 | semidirect |
| 4. #26018440 | C2 | semidirect |
| 5. #26018439 | C2 | semidirect |
| 6. #26018438 | C2 | semidirect |
| 7. C89×#1418 | C2 | semidirect |
| 9. #19152031 | C4 | semidirect |
| 13. #19152027 | C4 | semidirect |
| 14. Q32×D89 | C4 | semidirect |
| 16. D16×D89 | C4 | semidirect |
| 19. #19151432 | C22 | semidirect |
| 22. #19151426 | C22 | semidirect |
| 25. M64×C89 | C22 | semidirect |
| 26. #367×C89 | C22 | semidirect |
| 38. Dic712 | C2×C4 | semidirect |
| 43. D1424 | C2×C4 | semidirect |
| 54. Q32×C89 | C2×C4 | semidirect |
| 56. D16×C89 | C2×C4 | semidirect |
| 146. D89 | #1418 | direct (N × H) |
| 153. #1418 | D89 | direct (N × H) |
| 154. C89 | C2×#1418 | semidirect |
| 169. M64 | C2×D89 | semidirect |
| 173. #367 | C2×D89 | semidirect |
| 188. Q32 | C4×D89 | semidirect |
| 195. D16 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #508×D89 | 2 |
| M64×D89 | 2 |
| #367×D89 | 2 |
| #26018440 | 2 |
| #26018439 | 2 |
| #26018438 | 2 |
| C89×#1418 | 2 |
| C2×#1418 | 89 |