Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
548 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 119 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. #26018824 | C2 | semidirect |
| 4. #26018131 | C2 | semidirect |
| 16. #400×C89 | C4 | semidirect |
| 17. #399×C89 | C4 | semidirect |
| 18. #395×C89 | C4 | semidirect |
| 19. #393×C89 | C4 | semidirect |
| 201. C89 | #9385 | semidirect |
| 209. #400 | Dic89 | semidirect |
| 210. #399 | Dic89 | semidirect |
| 211. #395 | Dic89 | semidirect |
| 212. #393 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029281 | 2 |
| #26020240 | 2 |
| #26018824 | 2 |
| #26018131 | 2 |
| C89×#2564 | 2 |
| #9385 | 89 |