This study investigated whether clustering can identify different groups of students enrolled in a massive open online course (MOOC). This study applied self-organizing map and hierarchical clustering algorithms to the log files of a physics MOOC capturing how students solved weekly homework and quiz problems to identify clusters of students showing similar problem-solving patterns. The usefulness of the identified clusters was verified by examining various characteristics of students such as number of problems students attempted to solve, weekly and daily problem completion percentages, and whether they earned a course certificate. The findings of this study suggest that the clustering technique utilizing self-organizing map and hierarchical clustering algorithms in tandem can be a useful exploratory data analysis tool that can help MOOC instructors identify similar students based on a large number of variables and examine their characteristics from multiple perspectives.