Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
326 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 4. #89601 | C2 | semidirect |
| 6. #89454 | C2 | semidirect |
| 7. #89453 | C2 | semidirect |
| 8. #89453 | C2 | semidirect |
| 9. #89452 | C2 | semidirect |
| 186. C7 | #3231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90161 | 2 |
| C7×#431 | 2 |
| #89601 | 2 |
| #89495 | 2 |
| #89454 | 2 |
| #89453 | 2 |
| #89452 | 2 |
| #3231 | 7 |