Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
158 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 47 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. C2×Dic56 | C2 | semidirect |
| 4. #89645 | C2 | semidirect |
| 6. Dic7⋊C16 | C2 | semidirect |
| 7. #89287 | C2 | semidirect |
| 129. C7 | #2211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #89927 | 2 |
| C2×#6401 | 2 |
| C2×Dic56 | 2 |
| #89645 | 2 |
| C7×#357 | 2 |
| Dic7⋊C16 | 2 |
| #89287 | 2 |
| #2211 | 7 |