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Triangulum (M33) is the most massive satellite galaxy of Andromeda (M31),with a stellar mass of about $3\times10^9\; M_{\odot}$. Based on abundancematching techniques, M33's total mass at infall is estimated to be of order$10^{11}\; M_{\odot}$. $\Lambda$CDM simulations predict that M33-mass haloshost several of their own low mass satellite companions, yet only one candidateM33 satellite has been detected in deep photometric surveys to date. This`satellites of satellites' hierarchy has recently been explored in the contextof the dwarf galaxies discovered around the Milky Way's Magellanic Clouds inthe Dark Energy Survey. Here we discuss the number of satellite galaxiespredicted to reside within the virial radius ($\sim$160 kpc) of M33 based on$\Lambda$CDM simulations. We also calculate the expected number of satellitedetections in N fields of data using various ground--based imagers. Finally, wediscuss how these satellite population predictions change as a function ofM33's past orbital history. If M33 is on its first infall into M31's halo, itsproposed satellites are expected to remain bound to M33 today. However, if M33experienced a recent tidal interaction with M31, the number of survivingsatellites depends strongly on the distance achieved at pericenter due to theeffects of tidal stripping. We conclude that a survey extending to $\sim$100kpc around M33 would be sufficient to constrain its orbital history and amajority of its satellite population. In the era of WFIRST, surveys of thissize will be considered small observing programs.

$\Lambda$CDM Predictions for the Satellite Population of M33