  We systematically study the modifications in the couplings of the Higgs
boson, when identified as a pseudo Nambu-Goldstone boson of a strong sector, in
the light of LHC Run 1 and Run 2 data. For the minimal coset SO(5)/SO(4) of the
strong sector, we focus on scenarios where the standard model left- and
right-handed fermions (specifically, the top and bottom quarks) are either in 5
or in the symmetric 14 representation of SO(5). Going beyond the minimal 5L-5R
representation, to what we call here the 'extended' models, we observe that it
is possible to construct more than one invariant in the Yukawa sector. In such
models, the Yukawa couplings of the 125 GeV Higgs boson undergo nontrivial
modifications. The pattern of such modifications can be encoded in a generic
phenomenological Lagrangian which applies to a wide class of such models. We
show that the presence of more than one Yukawa invariant allows the gauge and
Yukawa coupling modifiers to be decorrelated in the 'extended' models, and this
decorrelation leads to a relaxation of the bound on the compositeness scale (f
> 640 GeV at 95% CL, as compared to f > 1 TeV for the minimal 5L-5R
representation model). We also study the Yukawa coupling modifications in the
context of the next-to-minimal strong sector coset SO(6)/SO(5) for
fermion-embedding up to representations of dimension 20. While quantifying our
observations, we have performed a detailed chi-square fit using the ATLAS and
CMS combined Run 1 and available Run 2 data.
