Common genetic variation has been associated with multiple symptoms in Autism Spectrum Disorder (ASD). However, our knowledge of shared genetic factor structures contributing to this highly heterogeneous neurodevelopmental condition is limited. Here, we developed a structural equation modelling framework to directly model genome-wide covariance across core and non-core ASD phenotypes, studying autistic individuals of European descent using a case-only design. We identified three independent genetic factors most strongly linked to language/cognition, behaviour and motor development, respectively, when studying a population-representative sample (N=5,331). These analyses revealed novel associations. For example, developmental delay in acquiring personal-social skills was inversely related to language, while developmental motor delay was linked to self-injurious behaviour. We largely confirmed the three-factorial structure in independent ASD-simplex families (N=1,946), but uncovered simplex-specific genetic overlap between behaviour and language phenotypes. Thus, the common genetic architecture in ASD is multi-dimensional and contributes, in combination with ascertainment-specific patterns, to phenotypic heterogeneity.