Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
432 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 109 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. #26019026 | C2 | semidirect |
| 5. #26018155 | C2 | semidirect |
| 6. #26018097 | C2 | semidirect |
| 7. C89×#1940 | C2 | semidirect |
| 166. #1940 | D89 | semidirect |
| 172. C89 | #8878 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028971 | 2 |
| #26019026 | 2 |
| #26018746 | 2 |
| #26018650 | 2 |
| #26018155 | 2 |
| #26018097 | 2 |
| C89×#1940 | 2 |
| #8878 | 89 |