Abstract: The automorphism group of a Cartan geometry of type (G,H) can be made into a Lie group, whose dimension is at most the dimension of the Lie group G. Its Lie algebra can be described in terms of the Lie algebra of G and the curvature of the geometry only.

We will show how this can be used to study possible dimensions of automorphism groups of parabolic geometries of a given type. Then we will use this to actually determine the second largest possible dimension of automorphism groups of regular parabolic geometries of some type. We will consider the cases, where G is SO(n + 1; n), G2, Sp(n + 1; 1) or Sp(6;R).