The short answer to your question is no, there is not dark matter between galaxies, at least at any appreciable level.
There is ordinary matter between galaxies, called the intergalactic medium (IGM). The IGM is an extremely dilute, hot gas that pervades the space between galaxies. The typical density of the IGM is about one hydrogen atom per cubic meter and its temperature is somewhere around 10^6 K. These high temperatures keep the IGM in pressure equilibrium with any galaxies and prevent it from collapsing onto galaxies.
Dark matter, however, is cold, and lacks the pressure support of the gas in the IGM, so it condenses onto galaxies.  One interesting difference between dark matter and ordinary matter is that dark matter lacks any sort of cooling mechanism. As a result, when ordinary matter collapses onto a galaxy, it can cool and condense into a relatively compact space and later form stars and planets. The dark matter, however, remains extended because it has no way to shed its gravitational potential energy. Galaxies therefore exhibit a substantial dark matter halo, where the ratio of dark matter to ordinary matter increases substantially a few galactic radii away from the center. Within the galaxy itself, ordinary matter is dominant by at least an order of magnitude, but the density of ordinary matter falls off exponentially while the dark matter falls off only with the cube of distance, leaving dark matter dominant a few galactic radii away from the galaxy.
One interesting question is whether or not dark matter halos exist in intergalactic space without a corresponding host galaxy at the center. As far as we can tell, the answer to that seems to be no, or at least, such structures must be quite small and exceedingly rare. There are dwarf galaxies (only 10^6 solar masses or so) which have enormous dark matter halos (much out of proportion to their size, relative to the Milky Way), but nearly every halo seems to have at least some ordinary matter present, no matter how feeble.
Cosmic voids are an even more extreme example. Voids are dominated by dark energy and therefore expand more rapidly than the rest of the universe. Voids tend to push any matter (dark or otherwise) into walls that separate them from surrounding voids. In a real sense, the universe is made of voids, and everything we know lies on the walls and filaments that separate them. This paper examined dark matter halos in cosmic voids and essentially found that there weren't any. In other words, they found that dark matter halos in cosmic voids have host galaxies just as often as dark matter halos outside of cosmic voids (which is to say, almost always).
: To be absolutely pedantic, I wouldn't doubt that there are a few dark matter particles whizzing about in intergalactic space. But I would be surprised if its density exceeded the (already puny) density of ordinary matter in the IGM.