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The alpha decay and heavy particle radioactivity of the isotopes of even–even superheavy nuclei with Z = 122–132 have been studied within Coulomb and proximity potential model. The predicted half-lives using our model are found to be in agreement with universal formula for cluster decay of Poenaru et al., the universal decay law of Qi et al., and the scaling law of Horoi et al., and most of the estimated values are well within the experimental upper limit (T1/2 < 1030 s). Our work targets the shell closure properties in the superheavy region. From the plots for log10(T1/2) against the neutron number of the daughter nuclei, three prominent minima are observed at N = 178, 184, and 194. The results show that in addition to N = 184, the neutron numbers N = 178 and 194 exhibit extra stability as compared to their neighbours. Based on these important observations, we have identified the possibility of N = 194 being a magic neutron number next to N = 184. Further, a new island of stability in the superheavy region has been predicted around the doubly magic 304120 superheavy nuclei and thus established the role of neutron shell closure in heavy particle decays very well.