Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
410 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 410 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 |
|---|---|---|
| 1. C7×#529 | C2 | semidirect |
| 2. #90168 | C2 | semidirect |
| 3. #89839 | C2 | semidirect |
| 4. #89837 | C2 | semidirect |
| 5. #89830 | C2 | semidirect |
| 6. #89827 | C2 | semidirect |
| 7. #89820 | C2 | semidirect |
| 8. #89810 | C2 | semidirect |
| 9. #89798 | C2 | semidirect |
| 10. #89786 | C2 | semidirect |
| 11. C2×#6377 | C2 | semidirect |
| 84. #529 | D7 | semidirect |
| 122. C7⋊C8 | #41 | semidirect |
| 248. C7 | #3180 | 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 |
| #89839 | 2 |
| #89837 | 2 |
| #89830 | 2 |
| #89827 | 2 |
| #89820 | 2 |
| #89810 | 2 |
| #89798 | 2 |
| #89786 | 2 |
| C2×#6377 | 2 |
| #3180 | 7 |