Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
260 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 6. C7×#125 | C4 | semidirect |
| 49. #125 | Dic7 | semidirect |
| 99. C7 | #1992 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#125 | 2 |
| #89707 | 2 |
| C2×#6377 | 2 |
| #89324 | 2 |
| #1992 | 7 |