Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
156 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 156 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. #89622 | C2 | semidirect |
| 4. #89451 | C2 | semidirect |
| 5. C7×#335 | C2 | semidirect |
| 7. #89276 | C2 | semidirect |
| 45. #335 | D7 | semidirect |
| 136. C7 | #1698 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #89622 | 2 |
| #89620 | 2 |
| #89466 | 2 |
| #89451 | 2 |
| C7×#335 | 2 |
| #89280 | 2 |
| #89276 | 2 |
| #1698 | 7 |