Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
834 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 834 conjugacy classes of subgroups — too many to draw. Only its 179 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. #26019410 | C2 | semidirect |
| 4. #26019348 | C2 | semidirect |
| 5. #26018990 | C2 | semidirect |
| 6. #26018707 | C2 | semidirect |
| 7. C89×#3556 | C2 | semidirect |
| 156. #3556 | D89 | semidirect |
| 163. C89 | #18698 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031635 | 2 |
| #26030577 | 2 |
| #26019410 | 2 |
| #26019348 | 2 |
| #26018990 | 2 |
| #26018707 | 2 |
| C89×#3556 | 2 |
| #18698 | 89 |