Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
362 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 113 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. #90422 | C2 | semidirect |
| 3. C7×#491 | C2 | semidirect |
| 4. #89857 | C2 | semidirect |
| 5. #89836 | C2 | semidirect |
| 6. #89589 | C2 | semidirect |
| 7. #89584 | C2 | semidirect |
| 8. #89579 | C2 | semidirect |
| 9. #89560 | C2 | semidirect |
| 10. #89485 | C2 | semidirect |
| 11. #89480 | C2 | semidirect |
| 73. #491 | D7 | semidirect |
| 198. C7 | #3174 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90422 | 2 |
| #90389 | 2 |
| C7×#491 | 2 |
| #89857 | 2 |
| #89836 | 2 |
| #89589 | 2 |
| #89584 | 2 |
| #89579 | 2 |
| #89560 | 2 |
| #89485 | 2 |
| #89480 | 2 |
| #3174 | 7 |