Let G be a finite group. The set of all prime divisors of the order of G is denoted by π(G). The Gruenberg-Kegel graph (the prime graph) Γ(G) of G is defined as the graph with the vertex set π(G) in which two different vertices p and q are adjacent if and only if G contains an element of order pq. If the order of G is even, then π1(G) denotes the connected component of Γ(G) containing 2. It is actual the problem of describing finite groups with disconnected Gruenberg-Kegel graphs. In the present article, all finite non-solvable groups G with 3 ∈ π(G)\π1(G) are determined.