Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
378 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26022048 | C2 | semidirect |
| 3. #26020378 | C2 | semidirect |
| 4. #26018262 | C2 | semidirect |
| 5. #26018261 | C2 | semidirect |
| 6. #26018260 | C2 | semidirect |
| 7. C89×#1347 | C2 | semidirect |
| 9. #19152002 | C4 | semidirect |
| 10. #19151973 | C4 | semidirect |
| 14. D8×Dic89 | C4 | semidirect |
| 15. #19151680 | C4 | semidirect |
| 179. #1347 | D89 | semidirect |
| 180. C89 | #11856 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030826 | 2 |
| #26022048 | 2 |
| #26020378 | 2 |
| #26018262 | 2 |
| #26018261 | 2 |
| #26018260 | 2 |
| C89×#1347 | 2 |
| #11856 | 89 |