Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
178 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 2. #89953 | C2 | semidirect |
| 3. C2×#6403 | C2 | semidirect |
| 6. C2×Dic56 | C2 | semidirect |
| 7. #89297 | C2 | semidirect |
| 134. C7 | #2251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×SD32 | 2 |
| #89953 | 2 |
| C2×#6403 | 2 |
| #89927 | 2 |
| C2×#6401 | 2 |
| C2×Dic56 | 2 |
| #89297 | 2 |
| #2251 | 7 |