How many combinations of partitions of a list can you make so that repetitions are minimised?

Well one line is not enough to capture that question so ill explain it here.

Earlier today i was in a zoom meet where there are 12 members and we were split into different breakout rooms. After 30 mins we were shuffled and the host made sure to use a different combinations such that no two people who were in the same breakout room was in the same breakout room now. The host atleast tried to minimize the repetitions.

So my question is how many such combinations can we make on a group such that no two people who were in a meeting earlier repeat themselves.

If you could tell me in a algorithmic way, i will understand it.