Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
388 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 115 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. #90421 | C2 | semidirect |
| 3. C7×#487 | C2 | semidirect |
| 4. #89862 | C2 | semidirect |
| 5. #89856 | C2 | semidirect |
| 6. #89588 | C2 | semidirect |
| 7. #89582 | C2 | semidirect |
| 8. #89577 | C2 | semidirect |
| 9. #89575 | C2 | semidirect |
| 10. C4×#1132 | C2 | semidirect |
| 11. #89460 | C2 | semidirect |
| 79. #487 | D7 | semidirect |
| 230. C7 | #3331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90421 | 2 |
| #90417 | 2 |
| C7×#487 | 2 |
| #89862 | 2 |
| #89856 | 2 |
| #89588 | 2 |
| #89582 | 2 |
| #89577 | 2 |
| #89575 | 2 |
| C4×#1132 | 2 |
| #89460 | 2 |
| #3331 | 7 |