Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
4390 conjugacy classes of subgroups; only the 651 normal subgroups are shown.
This group has 4390 conjugacy classes of subgroups — too many to draw. Only its 651 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. C2×#19151458 | C2 | semidirect |
| 2. #26018523 | C2 | semidirect |
| 3. #26018493 | C2 | semidirect |
| 10. C22×#41×C89 | C4 | semidirect |
| 52. C22×C4×C89 | C22⋊C4 | semidirect |
| 106. C89 | #14337 | semidirect |
| 108. C22×#41 | Dic89 | semidirect |
| 152. C22×C4 | C22⋊Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151458 | 2 |
| #26018523 | 2 |
| #26018493 | 2 |
| C23×#41×C89 | 2 |
| #14337 | 89 |