  The internal structure of the jets produced in neutral current interactions
for Q^2>125 GeV^2 has been studied using the subjet multiplicity with the ZEUS
detector at HERA. Jets are identified in the laboratory frame by applying the
longitudinally invariant k_T-cluster algorithm. Next-to-leading order QCD
calculations have been obtained and compared to the data; a good agreement has
been observed in the region where hadron-to-parton corrections are small,
E_{T,jet}> 25 GeV. In this region, the strong coupling constant is extracted
and the resulting value is alpha_s (M_Z)=0.1185 +/- 0.0016 (stat.)
^{+0.0067}_{-0.0048} (syst.) ^{+0.0089}_{-0.0071} (th.).
