Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
810 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 810 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 107. C22×Dic89 | Q16 | semidirect |
| 248. C89 | #9925 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151753 | 2 |
| #26026067 | 2 |
| C2×#19151519 | 2 |
| #26020188 | 2 |
| C2×#19151323 | 2 |
| #26018131 | 2 |
| C2×#328×C89 | 2 |
| #9925 | 89 |