Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
670 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 670 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 |
|---|---|---|
| 20. #533×C89 | C4 | semidirect |
| 21. C2×C4⋊Q8×C89 | C4 | semidirect |
| 22. #519×C89 | C4 | semidirect |
| 23. #519×C89 | C4 | semidirect |
| 179. C89 | #12724 | semidirect |
| 187. #533 | Dic89 | semidirect |
| 188. C2×C4⋊Q8 | Dic89 | semidirect |
| 189. #519 | Dic89 | semidirect |
| 190. #519 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021947 | 2 |
| #26021927 | 2 |
| #26021906 | 2 |
| #26020356 | 2 |
| C89×#3509 | 2 |
| #12724 | 89 |