Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
516 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 516 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 |
|---|---|---|
| 1. #26028890 | C2 | semidirect |
| 2. #26020329 | C2 | semidirect |
| 4. #26018105 | C2 | semidirect |
| 18. #390×C89 | C4 | semidirect |
| 19. #390×C89 | C4 | semidirect |
| 22. #384×C89 | C4 | semidirect |
| 23. #382×C89 | C4 | semidirect |
| 194. C89 | #9446 | semidirect |
| 203. #390 | Dic89 | semidirect |
| 204. #390 | Dic89 | semidirect |
| 207. #384 | Dic89 | semidirect |
| 208. #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 |
| #26018781 | 2 |
| #26018105 | 2 |
| C89×#2500 | 2 |
| #9446 | 89 |