"Second Cousins"

One set of Mary's grandparents had four children. Each of those children had four children and each of those children also had four children.

Assuming that all of these people are still alive, what is the lowest possible number of SECOND COUSINS each of Mary's children has?

Everyone in the family is the natural child of legally-married parents.

Second cousins are people who share the same great-grandparent (discounting siblings and first cousins).

Hint: The answer is NOT forty-eight.

"Second Cousins" is an original puzzle by Michael Daniels, first published 19th December 2011.