Phase diagrams for a random Ising antiferromagnet on Bethe-like lattices with triangular loops are obtained. Triangular loops cause strong geometrical frustration for the Ising antiferromagnet. Spin glass states appear by introducing randomness in the interaction between Ising spins. The random Ising antiferromagnet is studied by the replica method using global order parameter. The phase diagrams are compared with those for the corresponding random Ising ferromagnet to see the effects of the geometrical frustration. Antiferromagnetic phase does not appear for M <= 4 where M is the number of the corner sharing triangles on the Bethe-like lattices. In these cases, spin glass phase appears with a reentrant behavior. Spin glass phase in the random antiferromagnet appears for much weaker randomness than that in the corresponding random ferromagnet. (C) 2015 Elsevier B.V. All rights reserved.