Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
362 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 8. #89649 | C2 | semidirect |
| 9. #89647 | C2 | semidirect |
| 10. #89629 | C2 | semidirect |
| 11. #89626 | C2 | semidirect |
| 48. C2×Dic14 | Q8 | semidirect |
| 213. C7 | #3082 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90210 | 2 |
| #90207 | 2 |
| C7×#427 | 2 |
| C2×#6390 | 2 |
| #89874 | 2 |
| #89776 | 2 |
| #89767 | 2 |
| #89649 | 2 |
| #89647 | 2 |
| #89629 | 2 |
| #89626 | 2 |
| #3082 | 7 |