Let M be a closed orientable 3-manifold with a genus two Heegaard splitting (V1,V2;F) and a non-trivial JSJ-decomposition, where all components of the intersection of the JSJ-tori and Vi are not ∂-parallel in Vi for i=1,2. If G is a finite group of orientation-preserving diffeomorphisms acting on M which preserves each handlebody of the Heegaard splitting and each piece of the JSJ-decomposition of M, then G≅Z2 or D2 if Vj∩(∪Ti) consists of at most two disks or at most two annuli.