Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
416 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 8. #89647 | C2 | direct (N × H) |
| 41. C2×Dic14 | Q8 | semidirect |
| 86. Dic14 | C2×Q8 | semidirect |
| 150. C2×C7 | #477 | semidirect |
| 177. C7 | C2×#477 | semidirect |
| 191. C2 | #89647 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6451 | 2 |
| C2×#6450 | 2 |
| C2×C7×#107 | 2 |
| C2×#6390 | 2 |
| C2×Dic7⋊C8 | 2 |
| C2×#6384 | 2 |
| C2×#6381 | 2 |
| #89647 | 2 |
| C2×#477 | 7 |