We study the parameter space of the constrained exceptional supersymmetric standard model (cE 6SSM) consistent with a Higgs signal near 125GeV and the LHC searches for squarks, gluinos and Z ′. The cE 6SSM parameter space, consistent with correct electroweak symmetry breaking, is represented by scans in the (m 0,M 1/2) plane for fixed Z ′ mass and tanβ, with squark, gluino and Higgs masses plotted as contours in this plane. We find that a 125GeV 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 8TeV or forthcoming 14TeV runs. Successful dark matter relic abundance may be achieved over all the parameter space, assuming a binolike lightest supersymmetric particle 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 125GeV is provided which exemplifies these features.