A description is obtained for
the homeotopy group (the group of isotopy classes of homeomorphisms) of a compact
irreducible sufficiently large 3-manifold (which may contain 2-sided projective
planes). It is finitely presented, and modulo finite groups is either free, GL(3, ℤ), or is
built up in a certain way by extensions starting from 2-manifold homeotopy groups
and finitely generated abelian groups.