The two most popular ways to generate a topological manifold from others are picking a subspace of a topological space and computing the quotient space of a topological space. In differential geometry, it seems that looking at a subspace becomes far more popular than computing a quotient; an exemplary method is the preimage of a regular value of a differentiable function between manifolds.
Is there an analogue result/ theorem for under which conditions a quotient space of some (differentiable) manifold is itself a (differentiable) manifold, the same way the regular value theorem spells out some conditions for which a subset of a differentiable manifold is itself a differentiable manifold?