Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 2. #90418 | C2 | semidirect |
| 3. C7×#487 | C2 | semidirect |
| 4. #89863 | C2 | semidirect |
| 5. #89855 | C2 | semidirect |
| 6. #89587 | C2 | semidirect |
| 7. #89584 | C2 | semidirect |
| 8. #89578 | C2 | semidirect |
| 9. #89574 | C2 | semidirect |
| 10. C4×#1132 | C2 | semidirect |
| 11. #89460 | C2 | semidirect |
| 79. #487 | D7 | semidirect |
| 230. C7 | #3329 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90425 | 2 |
| #90418 | 2 |
| C7×#487 | 2 |
| #89863 | 2 |
| #89855 | 2 |
| #89587 | 2 |
| #89584 | 2 |
| #89578 | 2 |
| #89574 | 2 |
| C4×#1132 | 2 |
| #89460 | 2 |
| #3329 | 7 |