Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
530 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 530 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 |
|---|---|---|
| 3. #26018772 | C2 | semidirect |
| 4. #26018104 | C2 | semidirect |
| 16. #398×C89 | C4 | semidirect |
| 18. #397×C89 | C4 | semidirect |
| 19. #395×C89 | C4 | semidirect |
| 21. #393×C89 | C4 | semidirect |
| 190. C89 | #9184 | semidirect |
| 198. #398 | Dic89 | semidirect |
| 200. #397 | Dic89 | semidirect |
| 201. #395 | Dic89 | semidirect |
| 203. #393 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029293 | 2 |
| C4×#15667927 | 2 |
| #26018772 | 2 |
| #26018104 | 2 |
| C89×#2638 | 2 |
| #9184 | 89 |