Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
714 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 2. C2×#19151393 | C2 | semidirect |
| 3. #26020360 | C2 | semidirect |
| 15. #536×C89 | C4 | semidirect |
| 17. #533×C89 | C4 | semidirect |
| 20. #519×C89 | C4 | semidirect |
| 22. C4×#41×C89 | C4 | semidirect |
| 175. C89 | #12728 | semidirect |
| 180. #536 | Dic89 | semidirect |
| 182. #533 | Dic89 | semidirect |
| 185. #519 | Dic89 | semidirect |
| 187. C4×#41 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021921 | 2 |
| C2×#19151393 | 2 |
| #26020360 | 2 |
| C89×#3510 | 2 |
| #12728 | 89 |