$\mathbb{Q}$-representation and Galois theory

Question

Let $G=\mathbb{Z}/n\mathbb{Z}$, we know that all irreducible $\mathbb{Q}$-representation of $G$ is all the subfields of the cyclotomic extension $\mathbb{Q} [\zeta_n]/\mathbb{Q}$, but we know that $\mathrm{Gal} (\mathbb{Q} [\zeta_n ]/\mathbb{Q})\cong (\mathbb{Z} /n\mathbb{Z} )^{\times}$, so I wonder are there a general correspondence between Galois subfields of Galois extensions and representations of some finite groups such that all the irreducible representations of the finite group are exactly all normal subfields of the Galois extension?