Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
512 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 135 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. #26030911 | C2 | semidirect |
| 2. #26022471 | C2 | semidirect |
| 3. #26022428 | C2 | semidirect |
| 4. #26022333 | C2 | semidirect |
| 6. #26022143 | C2 | semidirect |
| 7. #26022068 | C2 | semidirect |
| 11. #19152000 | C22 | semidirect |
| 12. #19151978 | C22 | semidirect |
| 16. #19151706 | C22 | semidirect |
| 18. #19151422 | C22 | semidirect |
| 19. #19151419 | C22 | semidirect |
| 20. #19151413 | C22 | semidirect |
| 23. #19151376 | C22 | semidirect |
| 169. C89 | #33693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030911 | 2 |
| #26022471 | 2 |
| #26022428 | 2 |
| #26022333 | 2 |
| #26022203 | 2 |
| #26022143 | 2 |
| #26022068 | 2 |
| C89×#2955 | 2 |
| #33693 | 89 |