We study the fragmentation of the nearest high line-mass filament, the integral shaped filament (ISF, line-mass ~400M_{sun}_/pc) in the Orion A molecular cloud. We have observed a 1.6pc long section of the ISF with the Atacama Large Millimetre/submillimeter Array (ALMA) at 3mm continuum emission, at a resolution of ~3" (1200AU). We identify from the region 43 dense cores with masses about a solar mass. 60% of the ALMA cores are protostellar and 40% are starless. The nearest neighbour separations of the cores do not show a preferred fragmentation scale; the frequency of short separations increases down to 1200AU. We apply a two-point correlation analysis on the dense core separations and show that the ALMA cores are significantly grouped at separations below ~17000AU and strongly grouped below ~6000AU. The protostellar and starless cores are grouped differently: only the starless cores group strongly below ~6000AU. In addition, the spatial distribution of the cores indicates periodic grouping of the cores into groups of ~30000AU in size, separated by ~50000AU. The groups coincide with dust column density peaks detected by Herschel. These results show hierarchical, two-mode fragmentation in which the maternal filament periodically fragments into groups of dense cores. Critically, our results indicate that the fragmentation models for lower line-mass filaments (~16M_{sun}_/pc) fail to capture the observed properties of the ISF. We also find that the protostars identified with Spitzer and Herschel in the ISF are grouped at separations below ~17000AU. In contrast, young stars with disks do not show significant grouping. This suggests that the grouping of dense cores is partially retained over the protostar lifetime, but not over the lifetime of stars with disks. This is in agreement with a scenario where protostars are ejected from the maternal filament by the slingshot mechanism, a model recently proposed for the ISF. The separation distributions of the dense cores and protostars may also provide an evolutionary tracer of filament fragmentation.