The Force Concept Inventory is a multiple-choice test and is one of the most popular and most analyzed concept inventories. It is used to investigate student understanding of Newtonian mechanics. A structured approach to data analysis can transform it in a "diagnostic" instrument that can validate inferences about student thinking. In this paper, we show how cluster analysis methods can be used to investigate patterns of student conceptual understanding and supply useful details about the relationships among student concepts and misconceptions. The answers given to the FCI questionnaire by a sample of freshman engineering have been analyzed. The analysis takes into account the decomposition of the force concept into the conceptual dimensions suggested by the FCI authors and successive studies. Our approach identifies latent structures within the student response patterns and groups students characterized by similar correct answers, as well as by non-correct answers. These response patterns give us new insights into the relationships between the student force concepts and their ability to analyze motions. Our results show that cluster analysis proved to be a useful tool to identify latent structures within the student conceptual understanding. Such structures can supply diagnostic insights for classroom pedagogy and teaching approaches.