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. #90373 | C2 | semidirect |
| 2. C7×#495 | C2 | semidirect |
| 3. #89960 | C2 | semidirect |
| 4. Q16×Dic7 | C2 | semidirect |
| 5. #89946 | C2 | semidirect |
| 6. #89936 | C2 | semidirect |
| 8. D8×Dic7 | C2 | semidirect |
| 9. #89827 | C2 | semidirect |
| 10. #89461 | C2 | semidirect |
| 11. #89454 | C2 | semidirect |
| 74. #495 | D7 | semidirect |
| 212. C7 | #3175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90373 | 2 |
| C7×#495 | 2 |
| #89960 | 2 |
| Q16×Dic7 | 2 |
| #89946 | 2 |
| #89936 | 2 |
| #89929 | 2 |
| D8×Dic7 | 2 |
| #89827 | 2 |
| #89461 | 2 |
| #89454 | 2 |
| #3175 | 7 |