Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 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×#462 | C2 | semidirect |
| 4. #89960 | C2 | semidirect |
| 5. #89959 | C2 | semidirect |
| 6. #89853 | C2 | semidirect |
| 7. C4×#1143 | C2 | semidirect |
| 8. #89618 | C2 | semidirect |
| 9. #89606 | C2 | semidirect |
| 10. #89586 | C2 | semidirect |
| 11. #89576 | C2 | semidirect |
| 83. #462 | D7 | semidirect |
| 228. C7 | #3302 | 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×#462 | 2 |
| #89960 | 2 |
| #89959 | 2 |
| #89853 | 2 |
| C4×#1143 | 2 |
| #89618 | 2 |
| #89606 | 2 |
| #89586 | 2 |
| #89576 | 2 |
| #3302 | 7 |