  Macroscopic magnetic properties and microscopic magnetic structure of
Rb$_2$Mn$_3$(MoO$_4$)$_3$(OH)$_2$ (space group $Pnma$) are investigated by
magnetization, heat capacity and single-crystal neutron diffraction
measurements. The compound's crystal structure contains bond-alternating
[Mn$_3$O$_{11}$]$^{\infty}$ chains along the $b$-axis, formed by isosceles
triangles of Mn ions occupying two crystallographically nonequivalent sites
(Mn1 site on the base and Mn2 site on the vertex). These chains are only weakly
linked to each other by nonmagnetic oxyanions. Both SQUID magnetometry and
neutron diffraction experiments show two successive magnetic transitions as a
function of temperature. On cooling, it transitions from a paramagnetic phase
into an incommensurate phase below 4.5~K with a magnetic wavevector near ${\bf
k}_{1} = (0,~0.46,~0)$. An additional commensurate antiferromagnetically
ordered component arises with ${\bf k}_{2} = (0,~0,~0)$, forming a complex
magnetic structure below 3.5~K with two different propagation vectors of
different stars. On further cooling, the incommensurate wavevector undergoes a
lock-in transition below 2.3~K. The experimental results suggest that the
magnetic superspace group is $Pnma.1'(0b0)s0ss$ for the single-${\bf k}$
incommensurate phase and is $Pn'ma(0b0)00s$ for the 2-${\bf k}$ magnetic phase.
We propose a simplified magnetic structure model taking into account the major
ordered contributions, where the commensurate ${\bf k}_{2}$ defines the
ordering of the $c$-axis component of Mn1 magnetic moment, while the
incommensurate ${\bf k}_{1}$ describes the ordering of the $ab$-plane
components of both Mn1 and Mn2 moments into elliptical cycloids
