Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
204 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 3. #89896 | C2 | semidirect |
| 5. C7×#344 | C2 | semidirect |
| 6. #89354 | C2 | semidirect |
| 7. #89326 | C2 | semidirect |
| 51. #344 | D7 | semidirect |
| 151. C7 | #2081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #89903 | 2 |
| C2×#6397 | 2 |
| #89896 | 2 |
| #89773 | 2 |
| C7×#344 | 2 |
| #89354 | 2 |
| #89326 | 2 |
| #2081 | 7 |