Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
352 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 352 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 |
|---|---|---|
| 1. C7×#556 | C2 | semidirect |
| 3. #89859 | C2 | semidirect |
| 4. #89851 | C2 | semidirect |
| 5. #89820 | C2 | semidirect |
| 6. #89817 | C2 | semidirect |
| 7. C4×#1143 | C2 | semidirect |
| 8. #89793 | C2 | semidirect |
| 9. D4×C7⋊C8 | C2 | semidirect |
| 10. #89775 | C2 | semidirect |
| 11. #89770 | C2 | semidirect |
| 74. #556 | D7 | semidirect |
| 218. C7 | #3340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#556 | 2 |
| #90254 | 2 |
| #89859 | 2 |
| #89851 | 2 |
| #89820 | 2 |
| #89817 | 2 |
| C4×#1143 | 2 |
| #89793 | 2 |
| D4×C7⋊C8 | 2 |
| #89775 | 2 |
| #89770 | 2 |
| #3340 | 7 |