  We revisit a class of examples described in the original paper on biproducts,
expand the class, and provide a detailed analysis of the coalgebra and algebra
structures of many of these examples. Connections with the semisimple Hopf
algebras of dimension a power of two determined by Kashina are examined.
  The finite-dimensional non-trivial semisimple cosemisimple Hopf algebras we
construct are shown to be lower cosolvable. Some of these have one proper
normal Hopf subalgebra and are not lower solvable.
