Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
132 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 9. C2×C7×C16 | C4 | semidirect |
| 11. #6393 | C4 | semidirect |
| 50. C2×C16 | Dic7 | semidirect |
| 95. C7 | #1382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×C16 | 2 |
| C2×#6393 | 2 |
| #89878 | 2 |
| #1382 | 7 |