Let σ be any D-net of ideals of order n over a commutative local Bezoutian ring R and denote by G(σ) the corresponding net subgroup in the general linear group of degree n over R (RZhMat, 1977, 2A280). We give an explicit computation of the factor group G(σ)/E(σ), where E(σ) is the subgroup generated by all elementary transvections in G(σ).