Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
172 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 113. C3×C7 | #499 | semidirect |
| 146. C7 | #4878 | semidirect |
| 159. C3 | #89836 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#890 | 2 |
| #10620943 | 2 |
| #10620647 | 2 |
| C3×#6381 | 2 |
| #10620523 | 2 |
| #10620521 | 2 |
| Dic3×C7⋊C8 | 2 |
| #89836 | 3 |
| #4878 | 7 |