Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
466 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 151 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. #26022572 | C2 | semidirect |
| 3. #26022567 | C2 | semidirect |
| 4. #26022561 | C2 | semidirect |
| 5. C2×M64×C89 | C2 | semidirect |
| 10. #19152030 | C22 | semidirect |
| 11. C2×Dic712 | C22 | semidirect |
| 13. C2×D1424 | C22 | semidirect |
| 14. Dic1424 | C22 | semidirect |
| 15. #19151437 | C22 | semidirect |
| 16. D2848 | C22 | semidirect |
| 18. M64×C89 | C22 | semidirect |
| 19. C2×C32×C89 | C22 | semidirect |
| 98. C2×M64 | D89 | semidirect |
| 99. C89 | #33981 | semidirect |
| 112. M64 | C2×D89 | semidirect |
| 113. C2×C32 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152030 | 2 |
| #26022572 | 2 |
| #26022567 | 2 |
| #26022561 | 2 |
| C2×M64×C89 | 2 |
| #33981 | 89 |