Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
384 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 149 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. #89629 | C2 | direct (N × H) |
| 147. C2×C7 | #479 | semidirect |
| 173. C7 | C2×#479 | semidirect |
| 187. C2 | #89629 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6453 | 2 |
| C2×#6450 | 2 |
| C2×C7×#106 | 2 |
| C2×#6390 | 2 |
| C2×Dic7⋊C8 | 2 |
| C2×#6384 | 2 |
| C2×#6381 | 2 |
| #89629 | 2 |
| C2×#479 | 7 |