Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
186 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 57 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×#500 | C2 | semidirect |
| 2. #89865 | C2 | semidirect |
| 5. #89853 | C2 | semidirect |
| 7. #89249 | C2 | semidirect |
| 39. #500 | D7 | semidirect |
| 122. C7 | #1719 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#500 | 2 |
| #89865 | 2 |
| #89860 | 2 |
| #89857 | 2 |
| #89853 | 2 |
| #89466 | 2 |
| #89249 | 2 |
| #1719 | 7 |