Conjugate fields of algebraic element

Question

Let $K= \Bbb{Q}(\theta)$ be an algebraic number field of degree $n$ and let $\theta_1=\theta,\ldots,\theta_n$ be the conjugates of $\theta$ over $\Bbb{Q}$. Suppose that there are exactly $m$ distinct fields among $\Bbb{Q}(\theta_1),\ldots,\Bbb{Q}(\theta_n)$. Prove that $m$ divides $n$ and each field occurs $n/m$ times.