  An example of an extension of a completely simple semigroup U by a group H is
given which cannot be embedded into the wreath product of U by H. On the other
hand, every central extension of U by H is shown to be embeddable in the wreath
product of U by H, and any extension of U by H is proved to be embeddable in a
semidirect product of a completely simple semigroup V by H where the maximal
subgroups of V are direct powers of those of U.
