Dispatches rhymes with:
attaches, bache's, detaches, hatch's, hatches, match's, mismatches, snatches, thatches, attaches, avalanches, bache's, benches, bihac's, birch's, bitches, boches, branch's, breaches, broaches, brunches, bulfinch's, churches', coach's, coaches, cockroaches, couches, crunches, crutches, detaches, dyches, encroaches, enriches, entrenches, etches, fetches, finches, french's, funches, gingrich's, gingriches, glitches, goldfinches, goodrich's, greenwich's, h's, h.'s, hatch's, hatches, hitches, hunches, izetbegovic's, kasich's, leach's, leaches, leeches, lunches, lurches, lynch's, march's, marches, mastrich's, match's, milosevic's, mismatches, mladic's, mulches, nacogdoches, niches, ostriches, overreaches, perches, piech's, pitches, pooches, povich's, preaches, punches, ranch's, research's, researches, rich's, roaches, sandwiches, scotches, screeches, searches, slouches, snatches, starches, stitches, stopwatches, thatches, torches, trenches, twitches, welch's, wenches, which's, witch's, wrenches, wristwatches
Dispatches sounds like:
despotic, dispatch, disputes, dissipates