Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
392 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 392 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. #89838 | C2 | semidirect |
| 4. #89829 | C2 | semidirect |
| 5. #89821 | C2 | semidirect |
| 6. #89811 | C2 | semidirect |
| 7. #89799 | C2 | semidirect |
| 8. #89792 | C2 | semidirect |
| 9. #89787 | C2 | semidirect |
| 10. #89779 | C2 | semidirect |
| 11. #89696 | C2 | semidirect |
| 84. #529 | D7 | semidirect |
| 255. C7 | #3251 | 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 |
| #89838 | 2 |
| #89829 | 2 |
| #89821 | 2 |
| #89811 | 2 |
| #89799 | 2 |
| #89792 | 2 |
| #89787 | 2 |
| #89779 | 2 |
| #89696 | 2 |
| #3251 | 7 |