Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1102 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 139 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. #26018966 | C2 | semidirect |
| 2. #26018876 | C2 | semidirect |
| 3. #26018586 | C2 | semidirect |
| 5. #19151655 | C22 | semidirect |
| 211. C89 | #8522 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26018966 | 2 |
| #26018876 | 2 |
| #26018586 | 2 |
| C2×#535×C89 | 2 |
| #8522 | 89 |