Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
560 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 5. C22×C4×Dic89 | C4 | semidirect |
| 8. C2×#15667919 | C4 | semidirect |
| 10. #19151365 | C4 | semidirect |
| 14. #323×C89 | C4 | semidirect |
| 217. C89 | #7213 | semidirect |
| 228. #323 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020326 | 2 |
| #26018489 | 2 |
| C89×#1462 | 2 |
| #7213 | 89 |