  A covering number of a family is the size of the smallest set that intersects
all sets from the family. In 1978 Frankl determined for $n\ge n_0(k)$ the
largest intersecting family of $k$-element subsets of $[n]$ with covering
number $3$. In this paper, we essentially settle this problem, showing that the
same family is extremal for any $k\ge 100$ and $n>2k$.
