Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
464 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 81 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. #26021234 | C2 | semidirect |
| 4. #26018764 | C2 | semidirect |
| 6. #26018162 | C2 | semidirect |
| 7. C89×#3237 | C2 | semidirect |
| 193. #3237 | D89 | semidirect |
| 199. C89 | #10215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031635 | 2 |
| #26031259 | 2 |
| #26021234 | 2 |
| #26018764 | 2 |
| #26018761 | 2 |
| #26018162 | 2 |
| C89×#3237 | 2 |
| #10215 | 89 |