Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
162 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 51 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×#462 | C2 | semidirect |
| 4. #89796 | C2 | semidirect |
| 5. #89342 | C2 | semidirect |
| 7. #89275 | C2 | semidirect |
| 43. #462 | D7 | semidirect |
| 140. C7 | #1702 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#462 | 2 |
| #89860 | 2 |
| #89799 | 2 |
| #89796 | 2 |
| #89342 | 2 |
| #89280 | 2 |
| #89275 | 2 |
| #1702 | 7 |