We present 3.7 arcsec (∼ 0.05 pc) resolution 3.2 mm dust continuum observations from the Institut de Radioastronomie Millimétrique Plateau de Bure Interferometer, with the aim of studying the structure and fragmentation of the filamentary infrared dark cloud (IRDC) G035.39 − 00.33. The continuum emission is segmented into a series of 13 quasi-regularly spaced (λ obs ∼ 0.18 pc) cores, following the major axis of the IRDC. We compare the spatial distribution of the cores with that predicted by theoretical work describing the fragmentation of hydrodynamic fluid cylinders, finding a significant (factor of 8) discrepancy between the two. Our observations are consistent with the picture emerging from kinematic studies of molecular clouds suggesting that the cores are harboured within a complex network of independent sub-filaments. This result emphasizes the importance of considering the underlying physical structure, and potentially, dynamically important magnetic fields, in any fragmentation analysis. The identified cores exhibit a range in (peak) beam-averaged column density (3.6 × 10 23 cm −2 < N H,c < 8.0 ×10 23 cm −2 ), mass (8.1 M < M c < 26.1 M ), and number density (6.1 × 10 5 cm −3 < n H,c,eq < 14.7 × 10 5 cm −3 ). Two of these cores, dark in the mid-infrared, centrally-concentrated, monolithic (with no traceable substructure at our PdBI resolution), and with estimated masses of the order ∼ 20 − 25 M , are good candidates for the progenitors of intermediate-to-high-mass stars. Virial parameters span a range 0.2 < α vir < 1.3. Without additional support, possibly from dynamically important magnetic fields with strengths of the order of 230 µG < B < 670 µG, the cores are susceptible to gravitational collapse. These results may imply a multilayered fragmentation process, which incorporates the formation of sub-filaments, embedded cores, and the possibility of further fragmentation.