Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
180 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 180 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 |
|---|---|---|
| 119. C3×C7 | #479 | semidirect |
| 154. C7 | #4796 | semidirect |
| 167. C3 | #89571 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic21 | 2 |
| #10620946 | 2 |
| C7×#835 | 2 |
| C3×#6409 | 2 |
| #10620523 | 2 |
| #10620522 | 2 |
| #10620518 | 2 |
| #89571 | 3 |
| #4796 | 7 |