  We give a necessary and sufficient condition for two Hopf algebras presented
as central extensions to be isomorphic, in a suitable setting. We then study
the question of isomorphism between the Hopf algebras constructed in
0707.0070v1 as quantum subgroups of quantum groups at roots of 1. Finally, we
apply the first general result to show the existence of infinitely many
non-isomorphic Hopf algebras of the same dimension, presented as extensions of
finite quantum groups by finite groups.
