The elements of the quotient group D 4 / R are R and ⁠ U = f v R ⁠. The group operation on the quotient is shown in the table. For example, ⁠ U ⋅ ⋅ U = f v R ⋅ ⋅ f v R = ( f v ⋅ ⋅ f v ) R = R ⁠. Both the subgroup R = { i d , r 1 , r 2 , r 3 } and the quotient D 4 / R are abelian, but D 4 is not. Sometimes a group can be reconstructed from a subgroup and quotient (plus some additional data), by the semidirect product construction; D 4 is an example.