Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
512 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
| 3. #26022472 | C2 | semidirect |
| 4. #26022429 | C2 | semidirect |
| 5. #26022334 | C2 | semidirect |
| 7. #26022145 | C2 | semidirect |
| 8. C89×#2166 | C2 | semidirect |
| 13. #19152000 | C22 | semidirect |
| 14. #19151978 | C22 | semidirect |
| 22. #19151706 | C22 | semidirect |
| 26. #19151421 | C22 | semidirect |
| 27. #19151415 | C22 | semidirect |
| 30. #364×C89 | C22 | semidirect |
| 32. #347×C89 | C22 | semidirect |
| 168. #2166 | D89 | semidirect |
| 169. C89 | #33693 | semidirect |
| 189. #364 | C2×D89 | semidirect |
| 193. #347 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030911 | 2 |
| #26029156 | 2 |
| #26022472 | 2 |
| #26022429 | 2 |
| #26022334 | 2 |
| #26022205 | 2 |
| #26022145 | 2 |
| C89×#2166 | 2 |
| #33693 | 89 |