Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
506 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
| 4. #26018252 | C2 | semidirect |
| 12. C2×C22⋊Q8×C89 | C4 | semidirect |
| 14. #397×C89 | C4 | semidirect |
| 16. #393×C89 | C4 | semidirect |
| 22. C4×C22⋊C4×C89 | C4 | semidirect |
| 205. C89 | #11845 | semidirect |
| 206. C2×C22⋊Q8 | Dic89 | semidirect |
| 209. #397 | Dic89 | semidirect |
| 211. #393 | Dic89 | semidirect |
| 218. C4×C22⋊C4 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020326 | 2 |
| C2×#19151322 | 2 |
| #26018273 | 2 |
| #26018252 | 2 |
| C89×#2561 | 2 |
| #11845 | 89 |