Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 3. C7×#427 | C2 | semidirect |
| 5. C2×#6390 | C2 | semidirect |
| 6. #89776 | C2 | semidirect |
| 7. #89767 | C2 | semidirect |
| 8. #89660 | C2 | semidirect |
| 9. #89656 | C2 | semidirect |
| 10. #89639 | C2 | semidirect |
| 11. #89634 | C2 | semidirect |
| 85. #427 | D7 | semidirect |
| 230. C7 | #3097 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90217 | 2 |
| #90214 | 2 |
| C7×#427 | 2 |
| #89882 | 2 |
| C2×#6390 | 2 |
| #89776 | 2 |
| #89767 | 2 |
| #89660 | 2 |
| #89656 | 2 |
| #89639 | 2 |
| #89634 | 2 |
| #3097 | 7 |