Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
448 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
| 15. #395×C89 | C4 | semidirect |
| 18. #382×C89 | C4 | semidirect |
| 156. C89 | #11717 | semidirect |
| 157. C2×C4⋊Q8 | Dic89 | semidirect |
| 163. #395 | Dic89 | semidirect |
| 166. #382 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26019985 | 2 |
| #26018566 | 2 |
| #26018273 | 2 |
| C89×#2628 | 2 |
| #11717 | 89 |