LetGbeafinitegroupandNanormalsubgroupofG.IfHisasubgroupofG/N,provethat1(H)isasubgroupinGoforderHN,where:GG/Nisthecanonicalhomomorphism.

\begin{array}{l}{\text { 14. Let } G \text { be a finite group and } N \text { a normal subgroup of } G . \text { If } H \text { is a subgroup of } G / N,} \\ {\text { prove that } \phi^{-1}(H) \text { is a subgroup in } G \text { of order }|H| \cdot|N|, \text { where } \phi : G ightarrow G / N \text { is the canonical }} \\ {\text { homomorphism. }}\end{array}