Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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. #90424 | C2 | semidirect |
| 2. C7×#498 | C2 | semidirect |
| 3. #89861 | C2 | semidirect |
| 4. #89641 | C2 | semidirect |
| 5. #89640 | C2 | semidirect |
| 7. #89636 | C2 | semidirect |
| 8. #89625 | C2 | semidirect |
| 9. #89624 | C2 | semidirect |
| 10. #89468 | C2 | semidirect |
| 11. #89461 | C2 | semidirect |
| 71. #498 | D7 | semidirect |
| 200. C7 | #3173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90424 | 2 |
| C7×#498 | 2 |
| #89861 | 2 |
| #89641 | 2 |
| #89640 | 2 |
| #89637 | 2 |
| #89636 | 2 |
| #89625 | 2 |
| #89624 | 2 |
| #89468 | 2 |
| #89461 | 2 |
| #3173 | 7 |