In this task, you are given a list. This list contains many lists of integers. The list is several items written within a []. Your task is to find the maximum number among the members of each inner list. The output should be a list comprised of the maximums with the same order as the internal lists.
[[-52, 39, 76, -20, -192, -127, 88], [-62, -19, 9, -96, -63, -71]]