Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
320 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 1. #26021941 | C2 | semidirect |
| 2. #26021927 | C2 | semidirect |
| 3. #26018427 | C2 | semidirect |
| 4. #26018409 | C2 | semidirect |
| 12. #540×C89 | C4 | semidirect |
| 15. #492×C89 | C4 | semidirect |
| 16. #491×C89 | C4 | semidirect |
| 22. #433×C89 | C4 | semidirect |
| 154. C89 | #13606 | semidirect |
| 155. #540 | Dic89 | semidirect |
| 158. #492 | Dic89 | semidirect |
| 159. #491 | Dic89 | semidirect |
| 165. #433 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021941 | 2 |
| #26021927 | 2 |
| #26018427 | 2 |
| #26018409 | 2 |
| C89×#3221 | 2 |
| #13606 | 89 |