  We use the description of the Schutzenberger automata for amalgams of finite
inverse semigroups given by Cherubini, Meakin, Piochi to obtain structural
results for such amalgams. Schutzenberger automata, in the case of amalgams of
finite inverse semigroups, are automata with special structure possessing
finite subgraphs, that contain all essential information related to the whole
automaton. Using this crucial fact, and the Bass-Serre theory, we show that the
maximal subgroups of an amalgamated free-product are either isomorphic to
certain subgroups of the original semigroups or can be described as fundamental
groups of particular finite graphs of groups build from the maximal subgroups
of the original semigroups.
