How many different ways are there to arrange 6 people in a round table?

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How many ways are there to seat six people around a circular table where two seatings are considered the same when everyone has the same two neighbors without regard to whether they are right or left neighbors?

I know we have to apply division rule. I also know by rotating at six position we overcount by factor of 6 but that gives me answer of 120, while the correct answer is 60.

How to solve this?