Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
706 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 706 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 3. #26018181 | C2 | semidirect |
| 67. C22×Dic89 | M16 | semidirect |
| 193. C89 | #11500 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151459 | 2 |
| #26018579 | 2 |
| #26018181 | 2 |
| C89×#1462 | 2 |
| #11500 | 89 |