Very little is known about the classification of finite subgroups of Cremona in dimension 3 over the field of complex numbers. Let G be an abelian subgroup. If it is isomorphic to a product of subgroups of Cr(1) and Cr(2), G is called of product type. If G is a cyclic extension of a group that acts on a K3 surface, then it is called of K3 type. In a joint work with Loginov and Zhang, we classified groups of K3 type and conjecture that these two types are the only ones that can occur in Cr(3).