Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
348 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 3. #89954 | C2 | semidirect |
| 7. #89647 | C2 | semidirect |
| 8. #89566 | C2 | semidirect |
| 9. #89565 | C2 | semidirect |
| 86. C2×Dic7 | Q16 | semidirect |
| 187. C7 | #3249 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90313 | 2 |
| C7×#467 | 2 |
| #89954 | 2 |
| #89888 | 2 |
| C2×Dic7⋊C8 | 2 |
| #89823 | 2 |
| #89647 | 2 |
| #89566 | 2 |
| #89565 | 2 |
| #3249 | 7 |