Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
474 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 18. #391×C89 | C4 | semidirect |
| 19. #391×C89 | C4 | semidirect |
| 22. #384×C89 | C4 | semidirect |
| 23. #382×C89 | C4 | semidirect |
| 176. C89 | #9444 | semidirect |
| 185. #391 | Dic89 | semidirect |
| 186. #391 | Dic89 | semidirect |
| 189. #384 | Dic89 | semidirect |
| 190. #382 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028890 | 2 |
| #26020329 | 2 |
| #26018785 | 2 |
| #26018105 | 2 |
| C89×#2499 | 2 |
| #9444 | 89 |