Design pattern to sort items in a specified direction using a sorting class

Codebase I am working in has several specialized sorting classes I want to reuse to support sorting in an api. For instance, a class called SortByHeight takes a list and sorts it in descending order, implementing custom logic before sorting.

I want clients to specify what direction they want to sort in, ascending or descending. The problem is that the SortBy* classes sort items in different orders by default, because that behavior makes sense in the context of the application. So the logic I am looking for is something like

1. Process and sort items with SortBy* class
2. Get the default sort order of the class
3. If it is different than the order specified in the api, reverse the sorted list

My current solution is store pairs of a SortBy* class, along with it's default sort direction in a static Map field of a different class.

Would extending the interface all SortBy* classes implement, by adding a getDirection abstract method be a better solution? This would potentially force SortBy* classes to specify the direction they sort in.