Among five persons \( D, E, F, G, H \), each having different heights, who is the second tallest?
Statements:
I. \( D \) is taller than only \( G \) and \( E \). \( F \) is not the tallest.
II. \( H \) is taller than \( F \). \( G \) is taller than \( E \) but shorter than \( D \).