Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
676 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26021226 | C2 | semidirect |
| 3. #26018873 | C2 | semidirect |
| 4. #26018873 | C2 | semidirect |
| 5. #26018791 | C2 | semidirect |
| 6. #26018791 | C2 | semidirect |
| 7. C89×#1556 | C2 | semidirect |
| 9. #19152323 | C4 | semidirect |
| 10. #19152322 | C4 | semidirect |
| 13. #19152263 | C4 | semidirect |
| 16. #19152251 | C4 | semidirect |
| 272. #1556 | D89 | semidirect |
| 277. C89 | #8499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034693 | 2 |
| #26021226 | 2 |
| #26018873 | 2 |
| #26018791 | 2 |
| C89×#1556 | 2 |
| #8499 | 89 |