Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
380 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 129 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. #89569 | C2 | semidirect |
| 9. #89564 | C2 | semidirect |
| 185. C7 | #3139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6507 | 2 |
| #90208 | 2 |
| C7×#419 | 2 |
| #89997 | 2 |
| #89892 | 2 |
| M16×Dic7 | 2 |
| #89776 | 2 |
| #89569 | 2 |
| #89564 | 2 |
| #3139 | 7 |