What do you mean by pit one group against other?

Generally, the phrase "to pit one (group) against the other" means to give them cause to focus their energies on battling one another, often to the benefit of some third party that needn't expend energy while the others weaken each other, placing the third party in an advantageous place.

In the arena of politics, this is often used by third-party candidates (Libertarians, for example) to refer to the act of letting Republicans and Democrats attack each other, which they usually do because of their status as the two leading political parties, allowing other parties to emerge looking pretty good in comparison to the muddy and bloody (figuratively) major candidates.

A related concept is the "wounded candidate". Sometimes, candidates from the same party will battle fiercely for their party's nomination in a primary election to represent that party in a general election against other parties. Occasionally, this campaigning becomes so fierce that the eventual winner cannot win due to all the negative publicity received during the primary campaign. The party here can be said to have been "pitted against themselves".