Quantum quenches in the Dicke model were studied both in the thermodynamic limit and the finite systems. For the integrable situation in the thermodynamic limit, the generalized Gibbs ensemble can effectively describe the energy-level occupations for the quench within the normal phase, but it fails for the quench to the superradiant phase. For the finite systems which are considered non-integrable, the post quench systems were studied by comparing with the thermal ensembles. The canonical ensembles are directly available for the quench within the normal phase. With the increasing of the target coupling strength over the equilibrium phase transition critical point, sudden changes take place for the effective temperature and the distance to the thermal ensembles. The thermalization was also studied by comparing with the results of the microcanonical ensembles.