The complete model number looks to be 110.22712100 making it a Whirlpool built 'direct drive' model.
** the problem I'm having is getting the top off so that I can replace the [lid switch]. **
I would imagine you would have trouble there since the top is NOT designed to come off of that design of washer. The whole cabinet is removed (or just tilted forward) for most internal component service (see the following link).