Subcarrier index modulation (SIM) is an interesting transmission technique that has been considered to improve the spectral efficiency and/or the error performance of orthogonal frequency-division multiplexing (OFDM) systems. The subcarriers are split into groups, and within each group part of the information is carried by an index associated with a selection of active subcarriers. Other techniques such as grouped linear constellation-precoding (GLCP) have also been applied. With GLCP, a diversity gain as large as the group size (in number of complex subcarriers) can be expected. In this paper, we propose to combine SIM and GLCP in a same scheme (GLCP-SIM), as an alternative to the well-known SIM with complex symbol interleaving (ISIM). Moreover, interleaving at real dimensions level and constellation rotations are also incorporated into the proposed scheme, potentially doubling the diversity gain. The good performance and the diversity gains are shown both through computer simulations and analysis.