Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
356 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 153 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 |
|---|---|---|
| 6. #89650 | C2 | semidirect |
| 7. #89646 | C2 | semidirect |
| 8. #89630 | C2 | semidirect |
| 9. #89627 | C2 | semidirect |
| 33. C2×C7×C8 | Q8 | semidirect |
| 48. C2×C7⋊C8 | Q8 | semidirect |
| 110. C2×C8 | Dic14 | semidirect |
| 143. C7 | #3160 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90208 | 2 |
| C7×#427 | 2 |
| #89878 | 2 |
| C2×C8×Dic7 | 2 |
| #89770 | 2 |
| #89650 | 2 |
| #89646 | 2 |
| #89630 | 2 |
| #89627 | 2 |
| #3160 | 7 |