Let $G=\left\langle g, h \mid h^{2}=1, g^{6}=1, h g h^{-1}=g^{-1}\right\rangle$ be the dihedral group of order 12 .

i) List all the subgroups of $G$ of order 2 . Which of them are normal?

ii) Now list all the remaining proper subgroups of $G$. [There are $6+3$ of them.]

iii) For each proper normal subgroup $N$ of $G$, describe the quotient group $G / N$.

iv) Show that $G$ is not isomorphic to the alternating group $A_{4}$.