Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
350 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 115 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. #90413 | C2 | semidirect |
| 3. C7×#477 | C2 | semidirect |
| 5. C4×#1144 | C2 | semidirect |
| 6. #89662 | C2 | semidirect |
| 7. #89661 | C2 | semidirect |
| 9. #89603 | C2 | semidirect |
| 10. #89570 | C2 | semidirect |
| 11. #89567 | C2 | semidirect |
| 78. #477 | D7 | semidirect |
| 217. C7 | #3375 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90413 | 2 |
| #90276 | 2 |
| C7×#477 | 2 |
| #89860 | 2 |
| C4×#1144 | 2 |
| #89662 | 2 |
| #89661 | 2 |
| #89620 | 2 |
| #89603 | 2 |
| #89570 | 2 |
| #89567 | 2 |
| #3375 | 7 |