I say there are five. Everything the Republican party does is done for some combination of the five power groups, typically about 2 of the 5; so long as progress is made on at least one front that each group cares about, each group puts up with the things they don't like about the others:

war against Muslims - neocons, theocons
general defense spending, war for oil - big business, neocons
low taxes - big business, libertarians
destroying safety net/public education - racists, libertarians, some theocons
undermining government regulation - big business, libertarians
law-and-order - neocons, racists, some theocons
anti-immigration - neocons, racists
pro-gun - libertarians, racists
anti-abortion, anti-teh-gay - theocons (and racists, who tend as a group to be homophobic and sexually controlling in addition to being racist)
appointing judges that enforce this sort of state - everybody