Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
654 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 654 conjugacy classes of subgroups — too many to draw. Only its 83 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. #26030201 | C2 | semidirect |
| 4. #26020349 | C2 | semidirect |
| 5. #26018786 | C2 | semidirect |
| 6. #26018106 | C2 | semidirect |
| 237. C89 | #9944 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030201 | 2 |
| #26025410 | 2 |
| #26024526 | 2 |
| #26020349 | 2 |
| #26018786 | 2 |
| #26018106 | 2 |
| C89×#1462 | 2 |
| #9944 | 89 |