Medulloblastoma, the most common malignant pediatric brain tumour, is currently treated with non-specific cytotoxic therapies including surgery, whole brain radiation, and aggressive chemotherapy. As medulloblastoma exhibits marked intertumoural heterogeneity, with at least four distinct molecular variants, prior attempts to identify targets for therapy have been underpowered due to small samples sizes. Here we report somatic copy number aberrations (SCNAs) in 1087 unique medulloblastomas. SCNAs are common in medulloblastoma, and are predominantly subgroup enriched. The most common region of focal copy number gain is a tandem duplication of the Parkinson’s disease gene SNCAIP, which is exquisitely restricted to Group 4α. Recurrent translocations of PVT1, including PVT1-MYC and PVT1-NDRG1 that arise through chromothripsis are restricted to Group 3. Numerous targetable SCNAs, including recurrent events targeting TGFβ signaling in Group 3, and NF-κB signaling in Group 4 suggest future avenues for rational, targeted therapy.