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In 1998, Mark Lewis posed a question which would strengthen the connection between the structure of a finite solvable group G and the set of its character degrees. Specifically, Lewis asked the following question: Lewis’ Question: Let G be a solvable group with cd(G)={1, a, b, c, ab, ac}, where a, b, and c are pairwise relatively prime positive integers. Must G = A × B, where cd(A)={1, a} and cd(B)={1, b, c}? To lend credibility to his question, Lewis verified it if a, b, and c are distinct primes. In this dissertation, we work on the structure of finite solvable groups whose character degree sets are in the form {1, a, b, c, ab, ac}, where a, b, and c are pairwise coprime integers. If p is a prime number and m is a positive integer greater than 1, then we say that the ordered pair (p,m) is a strongly coprime pair if m is not divisible by p and also p does not divide u-1, where 1 < u < m is any proper prime power divisor of m. We prove that: THEOREM. Let G be a solvable group with cd(G)={1, a, b, c, ab, ac}, where a, b, and c are pairwise relatively prime positive integers. Then dl(G)≤ 4, and if a is prime such that the pairs (a,b) and (a,c) are strongly coprime pairs, then one of the following holds: 1. G = A × B, where cd(A)={1, a} and cd(B)={1, b, c}. 2. There is a prime t such that G has a normal Sylow t-subgroup T with cd(T)={1, tl} for some integer l ≥ 2, ttl in {b, c}, and the Fitting height of G is at most 3.