  We study admissible transformations and Lie symmetries for a class of
variable-coefficient Burgers equations. We combine the advanced methods of
splitting into normalized subclasses and of mappings between classes that are
generated by families of point transformations parameterized by arbitrary
elements of the original classes. A nontrivial differential constraint on the
arbitrary elements of the class of variable-coefficient Burgers equations leads
to its partition into two subclasses, which are related to normalized classes
via families of point transformations parameterized by subclasses' arbitrary
elements. One of the mapped classes is proved to be normalized in the extended
generalized sense, and its effective extended generalized equivalence group is
found. Using the mappings between classes and the algebraic method of group
classification, we carry out the group classification of the initial class with
respect to its equivalence groupoid.
