Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
390 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 113 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. #90269 | C2 | semidirect |
| 3. C7×#460 | C2 | semidirect |
| 4. #89945 | C2 | semidirect |
| 5. #89939 | C2 | semidirect |
| 6. #89847 | C2 | semidirect |
| 7. #89803 | C2 | semidirect |
| 8. #89621 | C2 | semidirect |
| 9. #89607 | C2 | semidirect |
| 10. #89555 | C2 | semidirect |
| 11. #89537 | C2 | semidirect |
| 92. #460 | D7 | semidirect |
| 256. C7 | #3216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90407 | 2 |
| #90269 | 2 |
| C7×#460 | 2 |
| #89945 | 2 |
| #89939 | 2 |
| #89847 | 2 |
| #89803 | 2 |
| #89621 | 2 |
| #89607 | 2 |
| #89555 | 2 |
| #89537 | 2 |
| #3216 | 7 |