While the sound of a groan can vary depending on the context, the word itself is designed to mimic the sound of a low, mournful sound expressing pain, displeasure, or effort.
However, it's worth noting that the relationship between the word and the sound isn't always perfect. Some people might argue that "groan" doesn't perfectly capture the sound of a groan, especially in its various nuances.
Ultimately, the classification of "groan" as onomatopoeia depends on the individual's perception and understanding of the word.