Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
160 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
| 3. #89286 | C2 | semidirect |
| 4. C4×C7⋊C16 | C2 | semidirect |
| 26. #500 | D7 | semidirect |
| 87. C7 | #2240 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#500 | 2 |
| #89467 | 2 |
| #89286 | 2 |
| C4×C7⋊C16 | 2 |
| #2240 | 7 |