  Recently, emergent symmetry is one of fast-growing intriguing issues in
many-body systems. Its roles and consequential physics have not been well
understood in quantum phase transitions. Emergent symmetry of degenerate
groundstates is discussed in possible connection to spontaneous symmetry
breaking within the Landau theory. For a clear discussion, a quantum spin-$1/2$
plaquette chain system is shown to have rich emergent symmetry phenomena in its
groundstates. A covering symmetry group over all emergent symmetries
responsible for degenerate groundstates in the plaquette chain system is found
to correspond to a largest common symmetry group of constituent Hamiltonians
describing the plaquette system. Consequently, this result suggests that, as a
guiding symmetry principle in quantum phase transitions, {\it degenerate
groundstates are induced by a spontaneous breaking of symmetries belonging to a
largest common symmetry group of continent Hamiltonians describing a given
system but can have more symmetries than the largest common symmetry}.
