Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
362 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 87 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. #26020426 | C2 | semidirect |
| 5. #26018110 | C2 | semidirect |
| 6. #26018096 | C2 | semidirect |
| 7. C89×#1286 | C2 | semidirect |
| 155. #1286 | D89 | semidirect |
| 157. C89 | #10631 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021075 | 2 |
| #26020426 | 2 |
| #26018921 | 2 |
| #26018919 | 2 |
| #26018110 | 2 |
| #26018096 | 2 |
| C89×#1286 | 2 |
| #10631 | 89 |