  The N2HDM is based on the CP-conserving 2HDM extended by a real scalar
singlet field. Its enlarged parameter space and its fewer symmetry conditions
as compared to supersymmetric models allow for an interesting phenomenology
compatible with current experimental constraints, while adding to the 2HDM
sector the possibility of Higgs-to-Higgs decays with three different Higgs
bosons. In this paper the N2HDM is subjected to detailed scrutiny. Regarding
the theoretical constraints we implement tests of tree-level perturbativity and
vacuum stability. Moreover, we present, for the first time, a thorough analysis
of the global minimum of the N2HDM. The model and the theoretical constraints
have been implemented in ScannerS, and we provide N2HDECAY, a code based on
HDECAY, for the computation of the N2HDM branching ratios and total widths
including the state-of-the-art higher order QCD corrections and off-shell
decays. We then perform an extensive parameter scan in the N2HDM parameter
space, with all theoretical and experimental constraints applied, and analyse
its allowed regions. We find that large singlet admixtures are still compatible
with the Higgs data and investigate which observables will allow to restrict
the singlet nature most effectively in the next runs of the LHC. Similarly to
the 2HDM, the N2HDM exhibits a wrong-sign parameter regime, which will be
constrained by future Higgs precision measurements.
