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The supercharacter theories of $C_p \times C_2 \times C_2$ were classified inthe 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 isgenerated by automorphisms. We use this classification to give a precise countof the distinct supercharacter theories of $C_p\times C_2\times C_2$ anddescribe when a supercharacter theory can be constructed by more than onemethod. We also present an alternative proof of the classification using thelanguage of supercharacter theories.

An Enumeration of the Supercharacter Theories of $C_p \times C_2 \times C_2$ for Prime $p$