The tertiary subspace manifold was one of many domains located in the myriad layers of subspace. The solanogen-based lifeforms called the tertiary subspace manifold their home, which emits a subspace energy level of 16.2 keV.
In 2369, they tried to open a gateway between their domain and the regular universe by means of a spatial rupture created by sending spatially-inverted tetryons through a rift. They were stopped by the crew of the USS Enterprise-D before they could enter the universe, but were able to abduct some members of the crew into their domain, where they had formed a bubble of the regular universe and conducted experiments on the crew. (TNG: "Schisms")