Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
698 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 698 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 |
|---|---|---|
| 1. #26020326 | C2 | semidirect |
| 2. C2×#19151322 | C2 | semidirect |
| 3. #26018273 | C2 | semidirect |
| 4. #26018249 | C2 | semidirect |
| 12. C22×#41×C89 | C4 | semidirect |
| 15. #393×C89 | C4 | semidirect |
| 17. #392×C89 | C4 | semidirect |
| 22. #381×C89 | C4 | semidirect |
| 240. C89 | #11839 | semidirect |
| 241. C22×#41 | Dic89 | semidirect |
| 245. #393 | Dic89 | semidirect |
| 247. #392 | Dic89 | semidirect |
| 252. #381 | 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 |
| #26018249 | 2 |
| C89×#2404 | 2 |
| #11839 | 89 |