AbstractAA′₃B₄O₁₂ quadruple perovskites, with magnetic A′ and non-magnetic B cations, are characterized by a wide range of complex magnetic structures. These are due to a variety of competing spin-exchange interactions up to the fourth nearest neighbours. Here, we synthesize and characterize the magnetic behaviour of the CaCo₃Ti₄O₁₂ quadruple perovskite. We find that in the absence of an external magnetic field, the system undergoes antiferromagnetic ordering at 9.3 K. This magnetic structure consists of three interpenetrating mutually orthogonal magnetic sublattices. Under an applied magnetic field, this antiferromagnetic structure evolves into a canted ferromagnetic structure. In explaining these magnetic structures, as well as the seemingly unrelated magnetic structures found in other quadruple perovskites, we suggest a crucial role played by the underlying kagome lattices in these systems. All observed magnetic structures of these materials represent indeed one of the three possible ways to reduce spin frustration in the A′ site kagome layers. More specifically, our survey of the magnetic structures observed for quadruple perovskites AA′₃B₄O₁₂ reveals the following three ways to reduce spin frustration, namely to make each layer ferromagnetic, to adopt a compromise 120° spin arrangement in each layer, or to have a magnetic structure with a vanishing sum of all second nearest-neighbour spin exchanges.