A plasmonic dimer composed of a gold split ring and a gold disk is proposed. The scattering spectra and electromagnetic field distributions on the surface of the dimer are calculated by the finite difference time domain method, and the effects of split gap orientation and structural symmetry breaking of the ring on Fano resonance characteristics are theoretically investigated in detail. The results show the multiple Fano resonances that can be formed due to the destructive interference between the electric dipole mode of the disk and multiple multipolar modes of the split ring, and the red shift when the symmetry breaking of the split ring is broken. When the split gap of the ring is parallel to the interparticle axis of the dimer, multiple Fano resonances based on the odd-order mode and the even-order mode of the split ring can be generated, and more even-order Fano resonances can be formed due to the further symmetry breaking of the split ring. In addition, a more refined scattering spectrum can be obtained as the ring internal surface moves far away from the disk along the interparticle axis. On the other hand, Fano resonances based on the lower order multipolar modes of the ring can be increased as they move away from the split gap. When the split gap of the ring is perpendicular to the interparticle axis of the dimer, only the even-order Fano resonances can be excited, and these resonances increase with the ring internal surface going away from the disk no matter whether the split gap of the ring faces the disk or not. As the structural symmetry of the dimer is further broken due to the ring internal surface moving along the split gap direction, the odd-order Fano resonance can be successfully produced in the dimer with the split gap coming back to the disk, at the same time, the even-order Fano resonances are gradually weaken perhaps due to the complicated competitive behaviors of spectral overlapping between the dipole mode of the disk and multipolar mode of the ring in energy. However, there is no odd-order Fano resonance appearing in the dimer with the split gap facing the disk except for a slightly increased even-order Fano resonance, as the structural symmetry of the dimer is further broken. These results are expected to be useful in designing multiple Fano controllable split ring disk dimers and also developing the application of multiwavelength micro-nano photonics.