  We prove that if a normal subgroup of the extended mapping class group of a
closed surface has an element of sufficiently small support then its
automorphism group and abstract commensurator group are both isomorphic to the
extended mapping class group. The proof relies on another theorem we prove,
which states that many simplicial complexes associated to a closed surface have
automorphism group isomorphic to the extended mapping class group. These
results resolve the metaconjecture of N.V. Ivanov, which asserts that any
"sufficiently rich" object associated to a surface has automorphism group
isomorphic to the extended mapping class group, for a broad class of such
objects. As applications, we show: (1) right-angled Artin groups and surface
groups cannot be isomorphic to normal subgroups of mapping class groups
containing elements of small support, (2) normal subgroups of distinct mapping
class groups cannot be isomorphic if they both have elements of small support,
and (3) distinct normal subgroups of the mapping class group with elements of
small support are not isomorphic. Our results also suggest a new framework for
the classification of normal subgroups of the mapping class group.
