  DHOST inflation models where deviations from a pure de Sitter background are
induced by an axion-like potential can lead to large non-Gaussianities. We
investigate the nature of non-Gaussianities in these models and compare to the
results given by the Planck experiment. The overlap between the DHOST
non-Gaussianities and the equilateral, orthogonal and local templates can be
rendered arbitrarily small. On the other hand, this does not preclude DHOST
models from showing large non-Gaussianities as exemplified by their reduced
bispectrum. As a result, they could be probed by future experiments and also by
a more thorough analysis of the existing Planck data.
