For a nontrivial finite group G, the intersection graph \(\Gamma (G)\) of G is the simple undirected graph whose vertices are the nontrivial proper subgroups of G and two vertices are joined by an edge if and only if they have a nontrivial intersection. In a finite simple graph \(\Gamma \), the clique number of \(\Gamma \) is denoted by \(\omega (\Gamma )\). In this paper we show that if G is a finite group with \(\omega (\Gamma (G))<13\), then G is solvable. As an application, we characterize all non-solvable groups G with \(\omega (\Gamma (G))=13\). Moreover, we determine all finite groups G with \(\omega (\Gamma (G))\in \{2,3,4\}\).

对于非平凡有限群G ， G的交图\(\Gamma (G)\)是简单无向图，其顶点是G的非平凡真子群，并且两个顶点通过边连接当且仅当它们具有非平凡的交​​集。在有限简单图\(\Gamma \)中， \(\Gamma \)的团数用\(\omega (\Gamma )\)表示。在本文中，我们证明如果G是一个有限群且\(\omega (\Gamma (G))<13\)，则G是可解的。作为一个应用，我们用以下方式描述所有不可解群G\(\omega (\Gamma (G))=13\)。此外，我们用\(\omega (\Gamma (G))\in \{2,3,4\}\)确定所有有限群G。