Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
378 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26022010 | C2 | semidirect |
| 5. #26020377 | C2 | semidirect |
| 6. #26018366 | C2 | semidirect |
| 7. C89×#1381 | C2 | semidirect |
| 11. #19151719 | C4 | semidirect |
| 149. #1381 | D89 | semidirect |
| 150. C89 | #12829 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029168 | 2 |
| #26022010 | 2 |
| #26021999 | 2 |
| #26021960 | 2 |
| #26020377 | 2 |
| #26018366 | 2 |
| C89×#1381 | 2 |
| #12829 | 89 |