Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
160 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 4. #89307 | C2 | semidirect |
| 8. C7×M32 | C4 | semidirect |
| 10. C2×C7×C16 | C4 | semidirect |
| 13. #6386 | C4 | semidirect |
| 15. C2×C7⋊C16 | C4 | semidirect |
| 54. M32 | Dic7 | semidirect |
| 57. C2×C16 | Dic7 | semidirect |
| 101. C7 | #2110 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×M32 | 2 |
| #89873 | 2 |
| C2×#6386 | 2 |
| #89307 | 2 |
| #2110 | 7 |