Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
804 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 804 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 |
|---|---|---|
| 105. C22×Dic89 | Q16 | semidirect |
| 242. C89 | #9967 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151756 | 2 |
| C2×#19151753 | 2 |
| #26026368 | 2 |
| C2×#19151334 | 2 |
| #26018522 | 2 |
| #26018094 | 2 |
| C2×#328×C89 | 2 |
| #9967 | 89 |