We study mesoscopic fluctuations of the conductance through a quantum
dot at the wings of the Coulomb blockade peaks. At low temperatures, t
he main mechanism of conduction is elastic cotunneling. The conductanc
e strongly fluctuates with an applied magnetic field. The magnetic cor
relation field is shown to be controlled by the charging energy, and t
he correlation function has a universal form. The distribution functio
n for the conductance obtained analytically shows a nontrivial crossov
er between the orthogonal and unitary ensembles.