Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
390 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 4. #26018271 | C2 | semidirect |
| 5. #26018270 | C2 | semidirect |
| 6. #26018269 | C2 | semidirect |
| 7. C89×#1350 | C2 | semidirect |
| 181. #1350 | D89 | semidirect |
| 182. C89 | #11896 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #467×D89 | 2 |
| #26021861 | 2 |
| #26020289 | 2 |
| #26018271 | 2 |
| #26018270 | 2 |
| #26018269 | 2 |
| C89×#1350 | 2 |
| #11896 | 89 |