Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
310 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 77 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. #26020388 | C2 | semidirect |
| 4. #26018271 | C2 | semidirect |
| 5. #26018269 | C2 | semidirect |
| 157. C89 | #11861 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030817 | 2 |
| #26022048 | 2 |
| #26020388 | 2 |
| #26018271 | 2 |
| #26018269 | 2 |
| #26018267 | 2 |
| C89×#1349 | 2 |
| #11861 | 89 |