  We define several operations that switch substructures of Hadamard matrices
thereby producing new, generally inequivalent, Hadamard matrices. These
operations have application to the enumeration and classification of Hadamard
matrices. To illustrate their power, we use them to greatly improve the lower
bounds on the number of equivalence classes of Hadamard matrices in orders 32
and 36 to 3,578,006 and 18,292,717.
