Let $K/k$ be an unramified biquadratic extension of number fields (i.e., $\operatorname{Gal}(K/k)\simeq V_4$), and $k_1$, $k_2$ and $k_3$ its three intermediate fields. I know, in general, we can obtain the class numbers $h(K)$ of $K$ from the knowledge of $h(k_1)$, $h(k_2)$ and $h(k_3)$ (see the paper of **Yamamura Ken**: "Maximal unramified extensions of imaginary quadratic number fields of small conductors," **Lemma 2, p.418**).

My question is, can we get any information about $h(k_3)$ by knowing $h(k_1)$ and $h(k_2)$? For example, if we had a prime $p$ that divides $h(k_1)$ and $h(k_2)$ at the same time, can we say that $p$ divides $h(k_3)$ too? In general, I know there is no simple relation between them; I just want to know if we can get something when we add the condition of **unramification**.