Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
612 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 107 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. C23×Dic178 | C4 | semidirect |
| 12. #19151470 | C4 | semidirect |
| 14. #19151458 | C4 | semidirect |
| 49. #100×C89 | Q8 | semidirect |
| 182. C89 | #13293 | semidirect |
| 222. #100 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023617 | 2 |
| #26020240 | 2 |
| #26018371 | 2 |
| C4×#100×C89 | 2 |
| #13293 | 89 |