CoGalois groups appear in a natural way in the study of covers. They generalize the well-known group of covering automorphisms associated with universal covering spaces. Recently, it has been proved that each quasi-coherent sheaf over the projective line $\bm{P}^1(R)$ ($R$ is a commutative ring) admits a flat cover and so we have the associated coGalois group of the cover. In general the problem of computing coGalois groups is difficult. We study a wide class of quasi-coherent sheaves whose associated coGalois groups admit a very accurate description in terms of topological properties. This class includes finitely generated and cogenerated sheaves and therefore, in particular, vector bundles.