Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
374 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 115 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. #90275 | C2 | semidirect |
| 3. C7×#475 | C2 | semidirect |
| 4. #89850 | C2 | semidirect |
| 5. C4×#1143 | C2 | semidirect |
| 6. #89638 | C2 | semidirect |
| 7. #89633 | C2 | semidirect |
| 8. #89618 | C2 | semidirect |
| 9. #89610 | C2 | semidirect |
| 10. #89584 | C2 | semidirect |
| 11. #89581 | C2 | semidirect |
| 80. #475 | D7 | semidirect |
| 111. C7⋊C8 | #41 | semidirect |
| 222. C7 | #3353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90417 | 2 |
| #90275 | 2 |
| C7×#475 | 2 |
| #89850 | 2 |
| C4×#1143 | 2 |
| #89638 | 2 |
| #89633 | 2 |
| #89618 | 2 |
| #89610 | 2 |
| #89584 | 2 |
| #89581 | 2 |
| #3353 | 7 |