  We present a natural extension of the process of taking a group quotient to
arbitrary subgroups. We first review basic concepts from group theory. This
will allow us to see the relationship between our new, more general quotient
operation and the standard group quotient. In particular, we will find that a
naive attempt to perform the quotient process with a nonnormal subgroup
actually leads to a well-defined operation which can be easily characterized
with existing terminology.
