  On the triangular lattice, for $J_2/J_1$ between $1/8$ and $1$, the classical
Heisenberg model with first and second neighbor interactions presents
four-sublattice ordered ground-states. Spin-wave calculations of Chubukov and
Jolicoeur\cite{cj92} and Korshunov\cite{k93} suggest that quantum fluctuations
select amongst these states a colinear two-sublattice order. From theoretical
requirements, we develop the full symmetry analysis of the low lying levels of
the spin-1/2 Hamiltonian in the hypotheses of either a four or a two-sublattice
order. We show on the exact spectra of periodic samples ($N=12,16$ and $28$)
how quantum fluctuations select the colinear order from the four-sublattice
order.
