  In this paper we study algebraic structures of the classes of the $L_2$ analytic Fourier-Feynman transforms on Wiener space. To do this we first develop several rotation properties of the generalized Wiener integral associated with Gaussian processes. We then proceed to analyze the $L_2$ analytic Fourier-Feynman transforms associated with Gaussian processes. Our results show that these $L_2$ analytic Fourier--Feynman transforms are actually linear operator isomorphisms from a Hilbert space into itself. We finally investigate the algebraic structures of these classes of the transforms on Wiener space, and show that they indeed are group isomorphic. 
Algebraic structure of the $L_2$ analytic Fourier-Feynman transform   associated with Gaussian processes on Wiener space