For a prime p and a poset (1, 2) = (τ1, τ2 < τ3) of types, p-reduced almost completely decomposable groups with critical typeset (1, 2) and a p-power as regulating index are called (1, 2)-groups. The number of near-isomorphism types of indecomposable (1, 2)-groups depends on the exponent pk of the regulator quotient. It is shown that indecomposable (1, 2)-groups with a regulator quotient of exponent ≤ p3 have rank ≤4, and if the types τi and the prime p are fixed, then there are precisely four near-isomorphism types of indecomposable groups. It is unknown for which exponent pk0 of the regulator quotient exist infinitely many near-isomorphism types of indecomposable (1, 2)-groups. © 2008 Elsevier Inc. All rights reserved.