Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
456 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 181 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. #89645 | C2 | semidirect |
| 7. #89625 | C2 | semidirect |
| 13. C2×Dic28 | C4 | semidirect |
| 132. C7 | #2950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic28 | 2 |
| #90207 | 2 |
| C7×#427 | 2 |
| #89873 | 2 |
| #89776 | 2 |
| #89645 | 2 |
| #89625 | 2 |
| #2950 | 7 |