1. The problem statement, all variables and given/known data Find a direct product representation for the quaternion group. Which are your options? 2. Relevant equations 3. The attempt at a solution Theorem: The internal direct product of normal subgroups forms a homomorphism of the group. https://proofwiki.org/wiki/Internal_Group_Direct_Product_of_Normal_Subgroups The quaternion group as 6 normal subgroups, 4 of which are proper. Lets suppose I only choose proper subgroups. The orders of these are 2,4,4,4. Then I can form the product (grouporder2)x(anyothergrouporder4) and assure myself that it is a isomorphism. Therefore, I've created a direct product representation. Is this correct?