Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
382 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
| 13. #400×C89 | C4 | semidirect |
| 18. #382×C89 | C4 | semidirect |
| 145. C89 | #11813 | semidirect |
| 146. C2×C4⋊Q8 | Dic89 | semidirect |
| 149. #400 | Dic89 | semidirect |
| 154. #382 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020329 | 2 |
| #26018586 | 2 |
| #26018276 | 2 |
| C89×#2628 | 2 |
| #11813 | 89 |