The notion of exponential Dowling structures is introduced, generalizing Stanley’s original theory of exponential structures. Enumerative theory is developed to determine the Möbius function of exponential Dowling structures, including a restriction of these structures to elements whose types satisfy a semigroup condition. Stanley’s study of permutations associated with exponential structures leads to a similar vein of study for exponential Dowling structures. In particular, for the extended -divisible partition lattice we show that the Möbius function is, up to a sign, the number of permutations in the symmetric group on elements having descent set . Using Wachs’ original -labeling of the -divisible partition lattice, the extended -divisible partition lattice is shown to be -shellable.