Summary: We obtain first-order equations for \(G_2\) holonomy of a wide class of metrics with \(S^3\times S^3\) principal orbits and \(\text{SU}(2)\times\text{SU}(2)\) isometry, using a method recently introduced by Hitchin. The new construction extends previous results, and encompasses all previously obtained first-order systems for such metrics. We also study various group contractions of the principal orbits, focusing on cases where one of the \(S^3\) factors is subjected to an Abelian, Heisenberg or Euclidean-group contraction. In the Abelian contraction, we recover some recently constructed \(G_2\) metrics with \(S^3\times T^3\) principal orbits. We obtain explicit solutions of these contracted equations in cases where there is an additional \(U(1)\) isometry. We also demonstrate that the only solutions of the full system with \(S^3\times T^3\) principal orbits that are complete and non-singular are either flat \(R^4\) times \(T^3\), or else the direct product of Eguchi-Hanson and \(T^3\), which is asymptotic to \(R^4/Z_2\times T^3\). These examples are in accord with a general discussion of isometric fibrations by tori which, as we show, in general split off as direct products. We also give some (incomplete) examples of fibrations of \(G_2\) manifolds by associative 3-tori with either \(T^4\) or \(K3\) as base.