Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
154 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 49 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. #89865 | C2 | semidirect |
| 5. C7×#333 | C2 | semidirect |
| 6. #89277 | C2 | semidirect |
| 7. #89275 | C2 | semidirect |
| 46. #333 | D7 | semidirect |
| 134. C7 | #1703 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #89865 | 2 |
| #89856 | 2 |
| #89618 | 2 |
| #89610 | 2 |
| C7×#333 | 2 |
| #89277 | 2 |
| #89275 | 2 |
| #1703 | 7 |