Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1090 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1090 conjugacy classes of subgroups — too many to draw. Only its 183 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 |
|---|---|---|
| 2. C2×#19152041 | C2 | semidirect |
| 3. #26029907 | C2 | semidirect |
| 4. #26022205 | C2 | semidirect |
| 5. #26021989 | C2 | semidirect |
| 6. C89×#2115 | C2 | semidirect |
| 15. C22×Dic356 | C22 | semidirect |
| 18. #19152041 | C22 | semidirect |
| 21. #19151856 | C22 | semidirect |
| 23. #19151636 | C22 | semidirect |
| 25. #19151409 | C22 | semidirect |
| 27. C2×M32×C89 | C22 | semidirect |
| 28. #349×C89 | C22 | semidirect |
| 203. #2115 | D89 | semidirect |
| 204. C89 | #33532 | semidirect |
| 220. C2×M32 | C2×D89 | semidirect |
| 226. #349 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26035026 | 2 |
| C2×#19152041 | 2 |
| #26029907 | 2 |
| #26022205 | 2 |
| #26021989 | 2 |
| C89×#2115 | 2 |
| #33532 | 89 |