Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
268 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 39 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. #26018188 | C2 | semidirect |
| 2. #26018139 | C2 | semidirect |
| 116. C89 | #7397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26018188 | 2 |
| #26018139 | 2 |
| C89×#2010 | 2 |
| #7397 | 89 |