Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
650 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 7. C2×#15667927 | C4 | semidirect |
| 9. #19151454 | C4 | semidirect |
| 12. C2×#99×C89 | C4 | semidirect |
| 178. C89 | #7310 | semidirect |
| 185. C2×#99 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020167 | 2 |
| C89×#1781 | 2 |
| #7310 | 89 |