We present an unbiased search for molecular hydrogen emission in the L1688 cloud within the rho Ophiuchi molecular cloud complex. Our near-infrared survey covers a connected region of extent 35'x35'. We detect several new H_2_ flows but the total number of detected outflows is low and is consistent with the paucity of Class 0 and Class 1 sources in the molecular cloud. From the spatial distribution, their collimation and the individual shapes of the bow shocks, we suggest possible candidates for the outflow sources. Most of the candidate driving sources are deeply embedded in dense cores of the molecular cloud. A very young outflow arises from the newly discovered Class 0 source MMS 126. Two major outflows in the NE-SW direction arise from the YLW 15 and YLW 16 Class I sources. Three additional outflows, which both extend over several arcminutes, arise from the Class I sources YLW 31 and YLW 52. Flow directions are generally NE-SW, perpendicular to the elongation directions of the cloud filaments. The apparent extents of molecular flows are related to either the widths of cloud filaments or to the separation between filaments. The estimated jet power needed to continuously drive and excite the detected portions of the shocked H_2_ outflows lies in the range 0.02-0.2L_{sun}_. Given the critical dependence on the environment, however, the total sizes and powers of the outflows may be considerably larger.