Let's analyze the pattern in the three-letter groups by looking at the position of each letter in the alphabet.
\[\begin{array}{rl} \bullet & \text{First Letter: H(8), J(10), L(12), N(14). This is an arithmetic progression with a common difference of +2. The next letter should be 14 + 2 = 16, which is P.} \\ \bullet & \text{Second Letter: E(5), G(7), I(9), K(11). This is also an arithmetic progression with a common difference of +2. The next letter should be 11 + 2 = 13, which is M.} \\ \bullet & \text{Third Letter: C(3), E(5), G(7), I(9). This is also an arithmetic progression with a common difference of +2. The next letter should be 9 + 2 = 11, which is K.} \\ \end{array}\]
Combining the next letters gives us PMK.