We present metamaterial-induced transparency (MIT) phenomena with enhanced magnetic fields in hybrid dielectric metamaterials. Using two hybrid structures of identical-dielectric-constant resonators (IDRs) and distinct-dielectric-constant resonators (DDRs), we demonstrate a larger group index (ng~354), better bandwidth-delay product (BDP~0.9) than metallic-type metamaterials. The keys to enable these properties are to excite either the trapped mode or the suppressed mode resonances, which can be managed by controlling the contrast of dielectric constants between the dielectric resonators in the hybrid metamaterials.