If there were only three electron groups around an atom, how would they be arranged?

There would be two electrons in the 1s orbital one oriented up and one oriented down. The other electron would be in the 1p orbital up or down. Remember that 1s can only hold 2 electrons at a time, and when it is filled there one electron is spinning up and the other is spinning down. After 1s, comes the 1p orbital which can hold 6 electrons. Until 3 electrons are spinning either up or down, the next one will have the next orientation.