the group itself will have order 4,|e|=1

for any element a, |a|=1 or 2 or 4

if |a|=1 then a=e

if there is an a such that |a|=4, than it would be a cyclic, thus isomorphic to Z(4), so it will also have subgroup of order 2.

if such element does not exist, then 3 elements will have order 2, that is, isomorphic to Z(2)*Z(2).

"classify"actually means classify the group up to isomorphism