Finite groups arising as Galois groups of maximal unramified extension of number fields

Question

I was wondering if it is known for which number fields the maximal unramified (non-abelian) extension is of finite degree or do we know the finite groups that arise as the Galois groups of these finite degree maximal unramified extensions.

I have seen the trivial group and the group of two elements as these Galois groups but not beyond that.

Thanks in advance.