  We examine magnetic structures of electron systems on an extended triangular
lattice that consists of two types of bond triangles with electron transfer
energies t_l and t'_l (l = 1, 2, and 3), respectively. We examine the ground
state in the mean-field theory when t_1 = t'_1, focusing on collinear states
with two sublattices. It is shown that when the imbalance of the spatial
anisotropies of the two triangles is large, up-up-down-down (uudd) phases are
stable, and the most likely ground states of the lambda-(BETS)_2FeCl_4 system
are the Neel state with the modulation vector (\pi/c,\pi/a) and a uudd state,
where c = a_1 = a'_1 and a = (a_2+a'_2)/2, with a_1, a_1', a_2, and a_2' being
the lattice constants of the bonds with t_1, t'_1, t_2, and t'_2, respectively.
These results are consistent with those from the classical spin system. In
addition, this study reveals behaviors near the quantum critical point, which
cannot be reproduced in the localized spin model. As the imbalance of the
spatial anisotropies increases, the U_c of the Neel state increases, and that
of the uudd state decreases. In the phase diagrams containing areas of the
paramagnetic state, the Neel state with (\pi/c,\pi/a), and a uudd state, their
boundaries terminate at a triple point, near which all the transitions are of
the first order. The phase boundary between the antiferromagnetic phases does
not depend on U, and the transition is of the first order everywhere on the
boundary. By contrast, the transitions from the two antiferromagnetic phases to
the paramagnetic phase are of the second order, unless the system is close to
the triple point.
