Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 121 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. C7×#529 | C2 | semidirect |
| 2. #90168 | C2 | semidirect |
| 3. #89840 | C2 | semidirect |
| 4. #89831 | C2 | semidirect |
| 5. #89819 | C2 | semidirect |
| 6. #89809 | C2 | semidirect |
| 7. #89803 | C2 | semidirect |
| 8. #89799 | C2 | semidirect |
| 9. #89791 | C2 | semidirect |
| 10. #89787 | C2 | semidirect |
| 11. #89697 | C2 | semidirect |
| 86. #529 | D7 | semidirect |
| 261. C7 | #3212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#529 | 2 |
| #90168 | 2 |
| #89840 | 2 |
| #89831 | 2 |
| #89819 | 2 |
| #89809 | 2 |
| #89803 | 2 |
| #89799 | 2 |
| #89791 | 2 |
| #89787 | 2 |
| #89697 | 2 |
| #3212 | 7 |