Non-divisible Factors Of 2016

Probability Level 5

Let $F$ be the set of all positive integer factors of 2016.

Let $S$ be a subset of $F$ with the following property:

For any pair of distinct elements $a$ and $b$ in $S$ , $a\nmid b$ and $b\nmid a$ .

What is the maximum value of $|S|$ ?