Ibn Buraydah reported from his father that the Prophet (may Allah's peace and blessings be upon him) appointed a sixth (of the inheritance) to the grandmother if there is no mother to inherit thereby excluding the grandmother from inheritance.
شرح الحديث :
This Hadīth shows that the grandmother's share of inheritance is one sixth, whether she is the mother's mother or the father's mother. Two or more grandmothers share one sixth if they are of the same degree. If they differ, then the closer grandmother inherits while the distant grandmother does not. For example, the mother's mother takes nothing when the mother is there. Also, the father's grandmother takes nothing when the father's mother is there.