In chronic lymphocytic leukemia (CLL) the interaction of leukemic cells with the microenvironment ultimately affects patient outcome. CLL cases can be divided in two subgroups with different clinical course based on the mutational status of the immunoglobulin heavy variable (IGHV) genes: mutated CLL (M-CLL) and unmutated CLL (U-CLL). Since in CLL, the differentiated relation of genes between the two subgroups is of greater importance than the individual gene behavior, this paper investigates the differences between the groups' gene interactions, by comparing their correlation structures. Fisher's test and Zou's confidence intervals are employed to detect differences of correlation coefficients. Afterwards, networks created by the genes participating in most differences are estimated with the use of structural equation models (SEM). The analysis is enhanced with graph modeling in order to visualize the between group differences in the gene structures of the two subgroups. The applied methodology revealed stronger correlations between genes in U-CLL patients, a finding in line with related biomedical literature. Using SEM for multigroup analysis, different gene structures between the two groups of patients were confirmed. The study of correlation structures can facilitate the detection of differential gene expression profiles in CLL subgroups, with potential applications in other diseases. Comparison of correlations can be very useful in understanding the complex internal structural differences which signify the variations of a disease.