The heavy particle decays that are probable from the isotopes of Z = 128 superheavy nuclei within the range A = 306–339 have been analyzed within the Coulomb and proximity potential model (CPPM). The study includes the evaluation of heavy particle decay half-lives of 24 clusters, including both odd and even clusters that are supposed to be emitted from the Z = 128 superheavy nuclei. The predicted values in comparison with the models Universal curve (UNIV), Universal decay law (UDL), and scaling law of Horoi et al. are observed to follow the same trend, and almost all the values lie well within the experimental limit (T1/2 <1030s). The interesting point of the study is the confirmation of the importance of neutron magicity in the superheavy region, noticed from the plots of log10(T1/2) vs. neutron number of the daughter nuclei. The minimum observed corresponds to the daughter nucleus with N = 184, which strongly supports the possibility of N = 184 to be a shell closure number. Also, the abrupt increase in the half-lives at A = 330 of the parent nuclei is the signature of neutron magicity at N = 202 associated with the parent nuclei. In addition, in the emission of odd mass clusters, the odd–even staggering (OES) effect is found which is more prominent in the case of heavy odd mass clusters. Importantly, the different slopes and intercepts obtained from the Geiger–Nuttall plots of log10(T1/2) vs. Q−1/2 confirming the presence of shell closure effect and the plot of universal curve of log10(T1/2) vs.−lnP revealed the reliability of the model CPPM.