Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
212 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 2. C7×#431 | C2 | semidirect |
| 3. #89697 | C2 | semidirect |
| 4. #89279 | C2 | semidirect |
| 5. #89278 | C2 | semidirect |
| 51. #431 | D7 | semidirect |
| 157. C7 | #1482 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90170 | 2 |
| C7×#431 | 2 |
| #89697 | 2 |
| #89279 | 2 |
| #89278 | 2 |
| #1482 | 7 |