  In positive characteristic, nearly all Picard-Vessiot extensions are
inseparable over some intermediate iterative differential extensions. In the
Galois correspondence, these intermediate fields correspond to nonreduced
subgroup schemes of the Galois group scheme. Moreover, the Galois group scheme
itself may be nonreduced, or even infinitesimal. In this article, we
investigate which finite group schemes occur as iterative differential Galois
group schemes over a given ID-field. For a large class of ID-fields, we give a
description of all occuring finite group schemes.
