  X-ray selected galaxy group samples are usually generated by searching for
extended X- ray sources that reflect the thermal radiation of the intragroup
medium. On the other hand, large radio galaxies that regularly occupy galaxy
groups also emit in the X-ray window, and their contribution to X-ray selected
group samples is still not well understood. In order to investigate their
relative importance, we have carried out a systematic search for non-thermal
extended X-ray sources in the COSMOS field. Based on the morphological
coincidence of X-ray and radio extensions, out of 60 radio galaxies, and \sim
300 extended X-ray sources, we find only one candidate where the observed
extended X-ray emission arises from non- thermal processes related to radio
galaxies. We present a detailed analysis of this source, and its environment.
Our results yield that external Inverse Compton emission of the lobes is the
dominant process that generates the observed X-ray emission of our extended
X-ray candidate, with a minor contribution from the gas of the galaxy group
hosting the radio galaxy. Finally, we show that finding only one potential
candidate in the COSMOS field (in a redshift range 0 < z < 6 and with radio
luminosity between 1025 and 1030 W/Hz) is consistent with expected X-ray-counts
arising from synchrotron lobes. This implies that these sources are not a
prominent source of contamination in samples of X-ray selected clusters/groups,
but they could potentially dominate the z > 1 cluster counts at the bright end
(S_X > 7 \cdot 10^-15 erg s^-1 cm^2).
