Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
326 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 72. Dic28 | Q8 | semidirect |
| 204. C7 | #3387 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90413 | 2 |
| #90412 | 2 |
| C7×#498 | 2 |
| #89866 | 2 |
| #89863 | 2 |
| #89629 | 2 |
| #89628 | 2 |
| #89626 | 2 |
| #89625 | 2 |
| C4×Dic28 | 2 |
| #89451 | 2 |
| #3387 | 7 |