Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
502 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 155 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. C2×#19152030 | C2 | semidirect |
| 2. C22×D1424 | C2 | semidirect |
| 3. #26022567 | C2 | direct (N × H) |
| 4. C2×#19151437 | C2 | semidirect |
| 5. C2×D2848 | C2 | semidirect |
| 6. C2×M64×C89 | C2 | semidirect |
| 10. #19152030 | C22 | semidirect |
| 11. C2×Dic712 | C22 | semidirect |
| 16. C2×D1424 | C22 | semidirect |
| 17. C2×D1424 | C22 | semidirect |
| 18. #19151437 | C22 | semidirect |
| 19. D2848 | C22 | semidirect |
| 21. M64×C89 | C22 | semidirect |
| 22. C2×C32×C89 | C22 | semidirect |
| 35. Dic712 | C23 | semidirect |
| 41. D1424 | C23 | semidirect |
| 47. C32×C89 | C23 | semidirect |
| 111. C2×C89 | #2263 | semidirect |
| 120. C2×M64 | D89 | semidirect |
| 121. C89 | C2×#2263 | semidirect |
| 136. M64 | C2×D89 | semidirect |
| 137. C2×C32 | C2×D89 | semidirect |
| 162. C32 | C22×D89 | semidirect |
| 227. C2 | #26022567 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152030 | 2 |
| C22×D1424 | 2 |
| #26022567 | 2 |
| C2×#19151437 | 2 |
| C2×D2848 | 2 |
| C2×M64×C89 | 2 |
| C2×#2263 | 89 |