Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1718 conjugacy classes of subgroups; only the 227 normal subgroups are shown.
This group has 1718 conjugacy classes of subgroups — too many to draw. Only its 227 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. #26020232 | C2 | semidirect |
| 2. C2×#19151342 | C2 | semidirect |
| 4. C2×C4⋊#10623494 | C22 | semidirect |
| 130. C22×C89 | #331 | semidirect |
| 152. C89 | #8339 | semidirect |
| 279. C22 | #19151342 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020232 | 2 |
| C2×#19151342 | 2 |
| C22×#127×C89 | 2 |
| #8339 | 89 |