Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
438 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 125 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×#532 | C2 | semidirect |
| 2. #90168 | C2 | semidirect |
| 3. #89865 | C2 | semidirect |
| 4. #89860 | C2 | semidirect |
| 5. #89848 | C2 | semidirect |
| 6. #89845 | C2 | semidirect |
| 7. #89809 | C2 | semidirect |
| 8. #89788 | C2 | semidirect |
| 9. #89697 | C2 | semidirect |
| 70. #532 | D7 | semidirect |
| 216. C7 | #3207 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#532 | 2 |
| #90168 | 2 |
| #89865 | 2 |
| #89860 | 2 |
| #89848 | 2 |
| #89845 | 2 |
| #89809 | 2 |
| #89788 | 2 |
| #89697 | 2 |
| #3207 | 7 |