An outstanding problem in the field of high-transition-temperature (high-Tc) superconductivity is the identification of the normal state out of which superconductivity emerges in the mysterious underdoped regime1. The normal state uncomplicated by thermal fluctuations can be studied using applied magnetic fields that are sufficiently strong to suppress long-range superconductivity at low temperatures2,3. Proposals in which the normal ground state is characterized by small Fermi surface pockets that exist in the absence of symmetry breaking1,4,5,6,7,8have been superseded by models based on the existence of a superlattice that breaks the translational symmetry of the underlying lattice7,8,9,10,11,12,13,14,15. Recently, a charge superlattice model that positions a small electron-like Fermi pocket in the vicinity of the nodes (where the superconducting gap is minimum)8,9,16,17has been proposed as a replacement for the prevalent superlattice models10,11,12,13,14that position the Fermi pocket in the vicinity of the pseudogap at the antinodes (where the superconducting gap is maximum)18. Although some ingredients of symmetry breaking have been recently revealed by crystallographic studies, their relevance to the electronic structure remains unresolved19,20,21. Here we report angle-resolved quantum oscillation measurements in the underdoped copper oxide YBa2Cu3O6 + x. These measurements reveal a normal ground state comprising electron-like Fermi surface pockets located in the vicinity of the nodes, and also point to an underlying superlattice structure of low frequency and long wavelength with features in common with the charge order identified recently by complementary spectroscopic techniques14,19,20,21,22.