Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1068 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 163 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. C2×#19152314 | C2 | semidirect |
| 2. #26030339 | C2 | semidirect |
| 3. #26019395 | C2 | semidirect |
| 4. #26019333 | C2 | semidirect |
| 5. #26018978 | C2 | semidirect |
| 6. #26018696 | C2 | semidirect |
| 7. C89×#3152 | C2 | semidirect |
| 16. #19151885 | C22 | semidirect |
| 17. #19151790 | C22 | semidirect |
| 21. #19151347 | C22 | semidirect |
| 22. #19151327 | C22 | semidirect |
| 27. #494×C89 | C22 | semidirect |
| 28. #492×C89 | C22 | semidirect |
| 168. #3152 | D89 | semidirect |
| 174. C89 | #18547 | semidirect |
| 186. #494 | C2×D89 | semidirect |
| 187. #492 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152314 | 2 |
| #26030339 | 2 |
| #26019395 | 2 |
| #26019333 | 2 |
| #26018978 | 2 |
| #26018696 | 2 |
| C89×#3152 | 2 |
| #18547 | 89 |