Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
714 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 267 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 |
|---|---|---|
| 1. #26020811 | C2 | semidirect |
| 105. C89 | #21913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020811 | 2 |
| #26020323 | 2 |
| #26020236 | 2 |
| C4×C22⋊#10623494 | 2 |
| C89×#2296 | 2 |
| #21913 | 89 |