Context. High-mass stars are formed as a result of the fragmentation of massive molecular clumps. However, what it is not clear is whether this fragmentation gives rise to stable prestellar cores massive enough to directly form high-mass stars or leads to prestellar cores of low masses that, by acquiring material from the environment, generate high-mass stars. Several recent observational studies focused on the characterisation of prestellar massive clump candidates. Nevertheless, studies of active massive clumps at different evolutionary stages are still needed to gain a complete understanding of how high-mass stars form. Aims. We present a comprehensive physical and chemical study of the fragmentation and star formation activity towards the massive clump AGAL G338.9188+0.5494, which harbours the extended green object EGO 338.92+0.55(b). The presence of an EGO embedded in a massive clump suggests that high-mass star formation is occurring at clump scale. The main goal of this work is to find evidence of such high-mass star formation, but at core scale. Methods. Using millimetre observations of continuum and molecular lines obtained from the Atacama Large Millimeter Array database at Bands 6 and 7, we study the substructure of the massive clump AGAL G338.9188+0.5494. The angular resolution of the data at Band 7 is about 0″.5, which allows us to resolve structures of about 0.01 pc (~2000 au) at the distance of 4.4 kpc. Results. The continuum emission at 340 GHz reveals that the molecular clump is fragmented into five cores, labelled C1 to C5. The 12CO J = 3−2 emission shows the presence of molecular outflows related to three of them. The molecular outflow related to core C1 is among the most massive (from 0.25 to 0.77 M⊙) and energetic (from 0.4 × 1046 to 1.2 × 1046 erg), considering studies carried out with similar observations towards this type of source. Rotational diagrams for the CH3CN and CH3CCH yield temperatures of about 340 and 72 K, respectively, for the core C1. The different temperatures show that the methyl cyanide would trace a gas layer closer to the protostar than the methyl acetylene, which would trace outermost layers. Using a range of temperatures going from 120 K (about the typical molecular desorption temperature in hot cores) to the temperature derived from CH3CN (about 340 K), the mass of core C1 ranges from 3 to 10 M⊙. The mid-IR 4.5 µm extended emission related to the EGO coincides in position and inclination with the discovered molecular outflow arising from core C1, which indicates that it should be the main source responsible for the 4.5 µm brightness. The average mass and energy of such a molecular outflow is about 0.5 M⊙ and 1046 erg, respectively, which suggest that 10 M⊙ is the most likely mass value for core C1. Additionally, we find that the region is chemically very rich with several complex molecular species. In particular, from an analysis of the CN emission, we find strong evidence that this radical is indirectly tracing the molecular outflows, or, more precisely, the border of the cavity walls carved out by such outflows, and therefore we point out that this is probably one of the first clear detection of CN as a tracer of molecular outflows in star-forming regions.