  We study the parameter space of the constrained exceptional supersymmetric
standard model (cE6SSM) consistent with a Higgs signal near 125 GeV and the LHC
searches for squarks, gluinos and Z'. The cE6SSM parameter space consistent
with correct electroweak symmetry breaking, is represented by scans in the (m0,
M1/2) plane for fixed Z' mass and tan beta, with squark, gluino and Higgs
masses plotted as contours in this plane. We find that a 125 GeV Higgs mass
only arises for a sufficiently large Z' mass, mostly above current limits, and
for particular regions of squark and gluino masses corresponding to multi-TeV
squark masses, but with lighter gluinos typically within reach of the LHC 8 TeV
or forthcoming 14 TeV runs. Successful dark matter relic abundance may be
achieved over all the parameter space, assuming a bino-like LSP with a nearby
heavier inert Higgsino doublet and decoupled inert singlinos, resulting in
conventional gluino decay signatures. A set of typical benchmark points with a
Higgs near 125 GeV is provided which exemplifies these features.
