  The zero-form and one-form global symmetries of the Aharony-Bergman-Jafferis
(ABJ) and related theories, with at least $\mathcal{N}=6$ supersymmetry in
three dimensions, are examined in detail. Starting from well-known dualities
between theories with orthogonal and symplectic gauge groups and those with
unitary gauge groups, we gauge their one-form symmetries or their subgroups and
obtain new dualities. One side of the latter involves theories with special
orthogonal and symplectic gauge groups, and the other side involves theories
with unitary gauge groups; there is a discrete quotient on one or both sides of
the duality. We study the refined superconformal indices of such theories and
map the symmetries across the dualities, with particular attention to their
discrete part. As a generalisation, we also find a new duality between a
circular quiver with a discrete quotient of alternating special orthogonal and
symplectic gauge groups and a three-dimensional $\mathcal{N}=4$ circular
(Kronheimer-Nakajima) quiver with unitary gauge groups, whose Higgs or Coulomb
branch describes an instanton on a singular orbifold.
