Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
728 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 139 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. #26021230 | C2 | semidirect |
| 3. #26018990 | C2 | semidirect |
| 15. #563×C89 | C4 | semidirect |
| 156. C89 | #8531 | semidirect |
| 157. #563 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021230 | 2 |
| #26021081 | 2 |
| #26018990 | 2 |
| #26018987 | 2 |
| C89×#3550 | 2 |
| #8531 | 89 |