New features of a previously introduced group approach to quantization are presented. We show that the construction of the symmetry group associated with the system to be quantized (the ‘‘quantizing group’’) does not require, in general, the explicit construction of the phase space of the system, i.e., does not require the actual knowledge of the general solution of the classical equations of motion; in many relevant cases an implicit construction of the group can be given, directly, on configuration space. To show an application, we construct the symmetry group for the conformally invariant massless scalar and electromagnetic fields and the scalar and Dirac fields evolving in a symmetric curved space-time or interacting with symmetric classical electromagnetic fields. Further generalizations of the present procedure are also discussed and in particular the conditions under which non-Abelian groups (mainly affine groups and more general gauge groups) can be included.