Background: Various cluster states of astrophysical interest are expected to exist in the excited states of 28 Si. However, they have not been identified firmly, because of the experimental and theoretical difficulties. Purpose: To establish the 24 Mg + α, 16 O + 12 C, and 20 Ne + 2α cluster bands, we theoretically search for the negative-parity cluster bands that are paired with the positive-parity bands to constitute the inversion doublets. We also offer the isoscalar monopole and dipole transitions as a promising probe for the clustering. We numerically show that these transition strengths from the ground state to the cluster states are very much enhanced.