Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
360 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 123 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. C7×#477 | C2 | semidirect |
| 4. #89863 | C2 | semidirect |
| 5. #89793 | C2 | semidirect |
| 7. #89646 | C2 | semidirect |
| 8. #89622 | C2 | semidirect |
| 11. #89564 | C2 | semidirect |
| 89. #477 | D7 | semidirect |
| 235. C7 | #3230 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D7×C4⋊Q8 | 2 |
| #90269 | 2 |
| C7×#477 | 2 |
| #89863 | 2 |
| #89793 | 2 |
| #89656 | 2 |
| #89646 | 2 |
| #89622 | 2 |
| #89605 | 2 |
| #89581 | 2 |
| #89564 | 2 |
| #3230 | 7 |