Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
346 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 346 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 |
|---|---|---|
| 2. #26020392 | C2 | semidirect |
| 5. #26018110 | C2 | semidirect |
| 6. #26018096 | C2 | semidirect |
| 7. C89×#1286 | C2 | semidirect |
| 153. #1286 | D89 | semidirect |
| 155. C89 | #10634 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021075 | 2 |
| #26020392 | 2 |
| #26018921 | 2 |
| #26018919 | 2 |
| #26018110 | 2 |
| #26018096 | 2 |
| C89×#1286 | 2 |
| #10634 | 89 |