The normalizer n of h in k is the largest subalgebra n of k which contains h as an ideal.  The normalizer of h always contains h itself.

SubalgebraNormalizer(h, k) calculates the normalizer of h in the subalgebra k.  If the second argument k is not specified, then the default is k = g and the normalizer h of  in g is calculated.

A list of vectors defining a basis for the normalizer of h is returned.

The command SubalgebraNormalizer is part of the DifferentialGeometry:-LieAlgebras package.  It can be used in the form SubalgebraNormalizer(...) only after executing the commands with(DifferentialGeometry) and with(LieAlgebras), but can always be used by executing DifferentialGeometry:-LieAlgebras:-SubalgebraNormalizer(...).