We present results from a spectroscopic survey of the dwarf spheroidal And XXII and the two extended clusters EC1 and EC2 .
These three objects are candidate satellites of the Triangulum galaxy , M33 , which itself is likely a satellite of M31 .
We use the DEep Imaging Multi-Object Spectrograph mounted on the Keck-II telescope to derive radial velocities for candidate member stars of these objects and thereby identify the stars that are most likely actual members .
Eleven most probable stellar members ( of 13 candidates ) are found for And XXII .
We obtain an upper limit of \sigma _ { v } < 6.0 { km s ^ { -1 } } for the velocity dispersion of And XXII , [ Fe/H ] \sim - 1.6 for its metallicity , and 255 { pc } for the Plummer radius of its projected density profile .
We construct a colour magnitude diagram for And XXII and identify both the red giant branch and the horizontal branch .
The position of the latter is used to derive a heliocentric distance to And XXII of 853 \pm 26 { kpc } .
The combination of the radial velocity , distance , and angular position of And XXII indicates that it is a strong candidate for being the first known satellite of M33 and one of the very few examples of a galactic satellite of a satellite .
N-body simulations imply that this conclusion is unchanged even if M31 and M33 had a strong encounter in the past few Gyr .
We test the hypothesis that the extended clusters highlight tidally stripped galaxies by searching for an excess cloud of halo-like stars in their vicinity .
We find such a cloud for the case of EC1 but not EC2 .
The three objects imply a dynamical mass for M33 that is consistent with previous estimates .