Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
322 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. C7×#477 | C2 | semidirect |
| 4. #89863 | C2 | semidirect |
| 5. #89792 | C2 | semidirect |
| 7. #89648 | C2 | semidirect |
| 8. #89623 | C2 | semidirect |
| 11. #89569 | C2 | semidirect |
| 86. #477 | D7 | semidirect |
| 229. C7 | #3237 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90419 | 2 |
| #90269 | 2 |
| C7×#477 | 2 |
| #89863 | 2 |
| #89792 | 2 |
| #89660 | 2 |
| #89648 | 2 |
| #89623 | 2 |
| #89607 | 2 |
| #89587 | 2 |
| #89569 | 2 |
| #3237 | 7 |