  It is shown that two dimensional (2d) topological gravity in the conformal
gauge has a larger symmetry than has been hitherto recognized; in the
formulation of Labastida, Pernici and Witten it contains a twisted ``small''
N=4 superconformal symmetry. There are in fact two distinct twisted N=2
structures within this N=4, one of which is shown to be isomorphic to the
algebra discussed by the Verlindes and the other corresponds, through
bosonization, to $c_M\leq 1$ string theory discussed by Bershadsky et.al. As a
byproduct, we find a twisted N=4 structure in $c_M\leq 1$ string theory. We
also study the ``mirror'' of this twisted N=4 algebra and find that it
corresponds, through another bosonization, to a constrained topological sigma
model in complex dimension one.
