Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
388 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 388 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 |
|---|---|---|
| 2. #90234 | C2 | semidirect |
| 3. C7×#436 | C2 | semidirect |
| 4. #89909 | C2 | semidirect |
| 5. #89905 | C2 | semidirect |
| 6. #89621 | C2 | semidirect |
| 7. #89614 | C2 | semidirect |
| 8. #89505 | C2 | semidirect |
| 9. #89493 | C2 | semidirect |
| 10. C4×#1132 | C2 | semidirect |
| 11. #89453 | C2 | semidirect |
| 86. #436 | D7 | semidirect |
| 230. C7 | #3331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90242 | 2 |
| #90234 | 2 |
| C7×#436 | 2 |
| #89909 | 2 |
| #89905 | 2 |
| #89621 | 2 |
| #89614 | 2 |
| #89505 | 2 |
| #89493 | 2 |
| C4×#1132 | 2 |
| #89453 | 2 |
| #3331 | 7 |