  The supercharacter theories of $C_p \times C_2 \times C_2$ were classified in
the language of Schur rings by Evdokimov, Kov\'acs, and Ponomarenko in [EKP16].
It was shown that every nontrivial supercharacter theory of $C_p \times C_2
\times C_2$ can be constructed as a wedge product, a direct product, or is
generated by automorphisms. We use this classification to give a precise count
of the distinct supercharacter theories of $C_p\times C_2\times C_2$ and
describe when a supercharacter theory can be constructed by more than one
method. We also present an alternative proof of the classification using the
language of supercharacter theories.
