Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
864 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 864 conjugacy classes of subgroups — too many to draw. Only its 151 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. #26020545 | C2 | semidirect |
| 2. #26018570 | C2 | semidirect |
| 148. C89 | #8317 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020545 | 2 |
| #26018570 | 2 |
| C89×#3459 | 2 |
| #8317 | 89 |