Permutations corresponding rigid motions of a rectangle/rhombus

Find the permutations that correspond to the rigid motions of a rectangle that is not a square. Do the same for the rigid motions of a rhombus that is not a square.

I began by drawing the rectangle and rhombus and labeling sides. I know I need to do something with permutations of the vertices. I feel like I need to do something with angles since they are not right angles, but I can not figure out what to do with angles.

Do I deal with angles at all? I know I need to do something with rotations and flips.