The demographics of dwarf galaxy populations have long been in tension with predictions from the Λ cold dark matter (ΛCDM) paradigm 1-4 . If primordial density fluctuations were scale-free as predicted, dwarf galaxies should themselves host dark-matter subhaloes 5 , the most massive of which may have undergone star formation resulting in dwarf galaxy groups. Ensembles of dwarf galaxies are observed as satellites of more massive galaxies 6-9 , and there is observational 10 and theoretical 11 evidence to suggest that these satellites at redshift z = 0 were captured by the massive host halo as a group. However, the evolution of dwarf galaxies is highly susceptible to environment 12-14 , making these satellite groups imperfect probes of ΛCDM in the low-mass regime. Here we report one of the clearest examples yet of hierarchical structure formation at low masses: using deep multi-wavelength data, we identify seven isolated, spectroscopically confirmed groups of only dwarf galaxies. Each group hosts three to five known members, has a baryonic mass of ~4.4 × 109 to 2 × 1010 solar masses (M ⊙), and requires a mass-to-light ratio of <100 to be gravitationally bound. Such groups are predicted to be rare theoretically and found to be rare observationally at the current epoch, and thus provide a unique window into the possible formation mechanism of more massive, isolated galaxies.