  We study the fragmentation of the nearest high line-mass filament, the
integral shaped filament (ISF, line-mass $\sim$ 400 M$_\odot$ pc$^{-1}$) in the
Orion A molecular cloud. We have observed a 1.6 pc long section of the ISF with
the Atacama Large Millimetre/submillimeter Array (ALMA) at 3 mm continuum
emission, at a resolution of $\sim$3" (1 200 AU). 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 1 200 AU. We apply a two-point correlation
analysis on the dense core separations and show that the ALMA cores are
significantly grouped at separations below $\sim$17 000 AU and strongly grouped
below $\sim$6 000 AU. The protostellar and starless cores are grouped
differently: only the starless cores group strongly below $\sim$6 000 AU. In
addition, the spatial distribution of the cores indicates periodic grouping of
the cores into groups of $\sim$30 000 AU in size, separated by $\sim$50 000 AU.
The groups coincide with dust column density peaks detected by Herschel. These
results show hierarchical, two-mode fragmentation in which the maternal
filament periodically fragments into groups of dense cores. Critically, our
results indicate that the fragmentation models for lower line-mass filaments
($\sim$ 16 M$_\odot$ pc$^{-1}$) 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 $\sim$17 000 AU. 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.
