Synonyms for Troika:

n.

group, duo, triumvirate, triune, foursome, pair, quartet, pairing, quintet, score, Triunity, four, couple, brace. coach, chariot, caravan, brougham, buggy, carriage, cart, cab, buckboard, chaise. three (noun)
triad, deltoid, trilogy, clover, trio, tripod, triangle, trimester, trident, delta, triplet, three, triple, triptych, ternary.
trio/triple (noun)
leash.
triune (noun)
triune.
troika (noun)
tierce, ternion, leash, triad, terzetto, deuce-ace, tercet, triangle, Triunity, iii, trio, three, triptych, triumvirate, triune, 3, trine, triple, trinity, ternary, trey, trilogy, triplet.

Other synonyms:

III
iii.
Triunity, triune, triumvirate. carriage. Other relevant words:
duo, couple, iii, trine, buggy, quintet, ternion, Triunity, group, deuce-ace, tercet, quartet, score, caravan, 3, coach, buckboard, brougham, ternary, triune, tierce, cab, terzetto, pair, four, carriage, trinity, chaise, triumvirate, trey, chariot, cart, foursome, pairing, brace, leash.