The Groth field is one of the sky regions that will be targeted by the OSIRIS Tunable Filter Emission Line Object survey in the optical 820 nm and 920 nm atmospheric windows. In the present paper, public Chandra X-ray data with total exposure time of 200 ks are analyzed and combined with optical broadband data of the Groth field, in order to study a set of optical structural parameters of the X-ray emitters and its relation with X-ray properties. To this aim, we processed the raw, public X-ray data using the Chandra Interactive Analysis of Observations, and determined and analyzed different structural parameters, in order to produce a morphological classification of X-ray sources. We present the morphology of 340 X-ray emitters with optical counterpart detected. Objects have been classified by X-ray type using a diagnostic diagram relating X-ray-to-optical ratio (X/O) to hardness ratio. We did not find any clear correlation between X-ray and morphological types. We analyzed the angular clustering of X-ray sources with optical counterpart using two-point correlation functions. A significant positive angular clustering was obtained from a preliminary analysis of four subsamples of the X-ray sources catalog. The clustering signal of the optically extended counterparts is similar to that of strongly clustered populations like red and very red galaxies, suggesting that the environment plays an important role in active galactic nuclei phenomena. Finally, we combined optical structural parameters with other X-ray and optical properties, and we confirmed an anticorrelation between the X/O ratio and the Abraham concentration index, which might suggest that early-type galaxies have lower Eddington rates than those of late-type galaxies.