Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
680 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 95 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. #26018273 | C2 | semidirect |
| 11. C23×Q8×C89 | C4 | semidirect |
| 16. #393×C89 | C4 | semidirect |
| 19. C2×#95×C89 | C4 | semidirect |
| 196. C89 | #11808 | semidirect |
| 197. C23×Q8 | Dic89 | semidirect |
| 203. #393 | Dic89 | semidirect |
| 207. C2×#95 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020326 | 2 |
| #26018579 | 2 |
| #26018273 | 2 |
| C2×#393×C89 | 2 |
| #11808 | 89 |