Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
462 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 462 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. #26033405 | C2 | semidirect |
| 2. #26033393 | C2 | semidirect |
| 3. #26022572 | C2 | semidirect |
| 4. #26022567 | C2 | semidirect |
| 5. #26022561 | C2 | semidirect |
| 6. C2×#19151437 | C2 | semidirect |
| 7. C89×#2258 | C2 | semidirect |
| 13. #19152030 | C22 | semidirect |
| 14. C2×Dic712 | C22 | semidirect |
| 16. Dic1424 | C22 | semidirect |
| 17. #19151437 | C22 | semidirect |
| 18. #19151437 | C22 | semidirect |
| 19. #19151437 | C22 | semidirect |
| 20. D2848 | C22 | semidirect |
| 22. M64×C89 | C22 | semidirect |
| 23. C2×C32×C89 | C22 | semidirect |
| 102. #2258 | D89 | semidirect |
| 103. C89 | #33983 | semidirect |
| 118. M64 | C2×D89 | semidirect |
| 119. C2×C32 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033405 | 2 |
| #26033393 | 2 |
| #26022572 | 2 |
| #26022567 | 2 |
| #26022561 | 2 |
| C2×#19151437 | 2 |
| C89×#2258 | 2 |
| #33983 | 89 |