The formation of three-dimensional magnetic ordering has been studied on a quasi-one-dimensional magnet

{CoNb}_{2} O_{6}

by mean-field calculations as well as neutron scattering measurements down to

T = 1.5 K

under magnetic fields up to

H_{∥ c} \sim 600 Oe .

Measurements of a deviation of the magnetic Bragg scattering function from the delta function in the ordered state reveal a surprisingly rich variety of the magnetic formation arising from an isosceles triangular arrangement of the magnetic chain with competing interchain interactions in the

a - b

plane. The competing interactions result in quasidegenerate ground states with different propagation wave numbers along the

b^{*}

direction in the sinusoidally amplitude-modulated incommensurate magnetic (IC) phase. Our mean-field calculations qualitatively reproduce the complicated

H_{∥ c} - T

magnetic phase diagram and give evidence for a high degeneracy of ground states by calculating the

H_{∥ c} - T

dependence of the free energy curve in the propagation wave number space. In addition, a partial cancellation of the exchange field at the apex site from the base sites on the isosceles triangular lattice leads to a quasi-long-range ordering along the a axis in both IC and antiferromagnetic states where the correlation length along the a axis depends on the propagation wave number along the

b^{*}

direction.

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