Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
706 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 706 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. #26018182 | C2 | semidirect |
| 62. C22×C4×C89 | M16 | semidirect |
| 137. C89 | #11500 | semidirect |
| 194. C22×C4 | #13083558 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26018579 | 2 |
| #26018182 | 2 |
| C2×#381×C89 | 2 |
| #11500 | 89 |