  The measure of the triple Higgs coupling is one of the major goals of the
high-luminosity run of the CERN Large Hadron Collider (HL-LHC) as well as the
future colliders, either leptonic such as the International Linear Collider
(ILC) or hadronic such as the 100 TeV Future Circular Collider in hadron-hadron
mode (FCC-hh). We have recently proposed this observable as a test of neutrino
mass generating mechanisms in a regime where heavy sterile neutrino masses are
hard to be probed otherwise. We present in this article a study of the one-loop
corrected triple Higgs coupling in the inverse seesaw model, taking into
account all relevant constraints on the model. This is the first study of the
impact on the triple Higgs coupling of heavy neutrinos in a realistic,
renormalizable neutrino mass model. We obtain deviations from the Standard
Model as large as to $\sim +30\%$ that are at the current limit of the HL-LHC
sensitivity, but would be clearly visible at the ILC or at the FCC-hh.
