Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
342 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 9. #19151322 | C4 | semidirect |
| 10. C22×M16×C89 | C4 | semidirect |
| 13. C2×C22⋊C8×C89 | C4 | semidirect |
| 151. C89 | #7320 | semidirect |
| 152. C22×M16 | Dic89 | semidirect |
| 157. C2×C22⋊C8 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020240 | 2 |
| #26018593 | 2 |
| C89×#1870 | 2 |
| #7320 | 89 |