  We review the notions of symplectic and orthogonal vector bundles over
curves, and the connection between principal parts and extensions of vector
bundles. We give a criterion for a certain extension of rank 2n to be
symplectic or orthogonal. We then describe almost all of its rank n vector
subbundles using graphs of sheaf homomorphisms, and give criteria for the
isotropy of these subbundles.
