Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 133 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×#520 | C2 | semidirect |
| 3. #90006 | C2 | semidirect |
| 4. #89775 | C2 | semidirect |
| 5. #89774 | C2 | semidirect |
| 6. #89768 | C2 | semidirect |
| 7. #89767 | C2 | semidirect |
| 8. #89743 | C2 | semidirect |
| 9. #89740 | C2 | semidirect |
| 10. #89738 | C2 | semidirect |
| 11. C2×#6382 | C2 | semidirect |
| 79. #520 | D7 | semidirect |
| 241. C7 | #3099 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#520 | 2 |
| #90524 | 2 |
| #90006 | 2 |
| #89775 | 2 |
| #89774 | 2 |
| #89768 | 2 |
| #89767 | 2 |
| #89743 | 2 |
| #89740 | 2 |
| #89738 | 2 |
| C2×#6382 | 2 |
| #3099 | 7 |