The synthesis of the new compounds R(15)Si(9)C with R = Sm, Gd-Er, Y and R(15)Ge(9)C with R = Ce, Pr and Nd has been recently reported; these compounds crystallize in the hexagonal La(15)Ge(9)Fe structure type, hP50-P6(3)mc, Z = 2 (ordered superstructure of La(5)Ge(3) (Mn(5)Si(3)-type, hP 16-P6(3)/mcm, Z = 2)). Here we report the results of a neutron diffraction investigation that we have performed to study the crystal and magnetic structures of the R(15)Si(9)C compounds with R = Tb, Ho and Er. All three compounds see the establishment of commensurate magnetic order with a predominantly ferromagnetic interaction. Details of mixed antiferro-ferromagnetic spin arrangements (κ = [000]) (for Tb(15)Si(9)C and Ho(15)Si(9)C) or of purely ferromagnetic ordering (Er(15)Si(9)C), and of their temperature dependence, are given and linked to the different coordination of the four dissimilar rare earth sites. In the Tb and Ho compounds the thermal evolution of the magnetic moment values strongly differs between the different R sites. The position occupied by the principal carbon has been determined (Wyckoff site 2b) and the existence of a second position available for the interstitial carbon (Wyckoff site 2a) has been revealed for R = Ho, Tb. Moreover, in the Tb and Ho compounds the magnetic moment value of the rare earth site R4, surrounding the second interstitial carbon site, is strongly reduced if compared to the value on the other rare earth sites. The magnetic transition temperatures of all three compounds, i.e. T(C) = 130, 43 and 45 K for Tb(15)Si(9)C, Ho(15)Si(9)C and Er(15)Si(9)C, are remarkably high compared to those of the parent R(5)Si(3) compounds. The magnetic behaviour of the partly filled Tb(5)Si(3)C(0.25) is reported.