Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
556 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 11. C2×C4⋊Q8×C89 | C4 | semidirect |
| 18. #384×C89 | C4 | semidirect |
| 19. C4×C4⋊C4×C89 | C4 | semidirect |
| 26. #15667927 | Q8 | semidirect |
| 180. C89 | #13298 | semidirect |
| 181. C2×C4⋊Q8 | Dic89 | semidirect |
| 190. #384 | Dic89 | semidirect |
| 192. C4×C4⋊C4 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020240 | 2 |
| C4×#15667927 | 2 |
| #26018377 | 2 |
| C89×#2542 | 2 |
| #13298 | 89 |