Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
744 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 744 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
| 227. C89 | #9957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151753 | 2 |
| #26023897 | 2 |
| #26021238 | 2 |
| #26020188 | 2 |
| #26018824 | 2 |
| #26018099 | 2 |
| C89×#3189 | 2 |
| #9957 | 89 |