The two-dimensional structures formed by monolayers and submonolayers of p-sexiphenyl (p-6P) molecules evaporated onto the Au(111) surface are investigated using ultrahigh vacuum scanning tunneling microscopy (UHV-STM). Five different 2D structures corresponding to different surface coverages are discovered and their 2D structures solved. The trends in the molecular alignment with respect to the underlying gold lattice are discussed. An unusual structure that consists of paired rows of p-6P molecules was discovered. A surface structure with alternating domains of slightly differently packed p-6P molecules was also found. The boundary between these two domains contains systematic molecular vacancies.