The three major groups of fungi are: 1  multicellular filamentous moulds. 2  macroscopic filamentous fungi that form large fruiting bodies. 3  Sometimes the group is referred to as ‘mushrooms’, but the mushroom is just the part of the fungus we see above ground which is also known as the fruiting body.ypes of fungi. Fungi are subdivided on the basis of their life cycles, the presence or structure of their fruiting body and the arrangement of and type of spores (reproductive or distributional cells) they produce.