An iterface does not have a parent class. It can have multiple "parent" interfaces, if it extends multiple interfaces.
As for a class that implements Map, you can't tell its parent class without knowing the class. Some classes may have Object as the parent class, implementing Map completely themselves. Others may extend AbstractMap, inheriting some methods from it. Others may even extend an existing Map implementation. An example is java.util.Properties, which extends java.util.Hashtable which in turn extends java.util.Dictionary which in turn extends Object. In this hierarchy, only Hashtable and Properties are Maps.