Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
520 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 520 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. #26030997 | C2 | semidirect |
| 3. #26022472 | C2 | semidirect |
| 4. #26022424 | C2 | semidirect |
| 5. #26022334 | C2 | semidirect |
| 7. #26022145 | C2 | semidirect |
| 8. C89×#2165 | C2 | semidirect |
| 13. #19151996 | C22 | semidirect |
| 14. #19151978 | C22 | semidirect |
| 23. #19151706 | C22 | semidirect |
| 26. #19151421 | C22 | semidirect |
| 27. #19151415 | C22 | semidirect |
| 30. #364×C89 | C22 | semidirect |
| 32. #347×C89 | C22 | semidirect |
| 169. #2165 | D89 | semidirect |
| 170. C89 | #33689 | semidirect |
| 190. #364 | C2×D89 | semidirect |
| 194. #347 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030997 | 2 |
| #26029163 | 2 |
| #26022472 | 2 |
| #26022424 | 2 |
| #26022334 | 2 |
| #26022205 | 2 |
| #26022145 | 2 |
| C89×#2165 | 2 |
| #33689 | 89 |