**Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 2.3 Exercise 2.3.7**

Let $Z_{48} = \langle x \rangle$ and use the isomorphism $\mathbb{Z}/(48) \cong Z_{48}$ given by $\overline{1} \mapsto x$ to list all subgroups of $Z_{48}$ as computed in Exercise 2.3.6.

Solution: