Coherent wave effects of thermal phonons hold promise of transformative opportunities in thermal transport control, but remain largely unexplored due to the small wavelength of thermal phonons, typically below a few nanometers. This small length scale indicates that, instead of artificial phononic crystals, a more promising direction is to examine the coherent phonon effects in natural materials with hierarchical superstructures matching the thermal phonon wavelength. In this work, we characterize the thermal properties of dodecagraphene (D-[BL1] graphene), a previously unstudied two-dimensional carbon allotrope based upon the traditional graphene structure but containing a secondary, in-plane periodicity. We use density functional theory (DFT) to calculate harmonic and anharmonic interatomic force constants (IFCs), which were then used to calculate the phonon dispersion, scattering rates, group velocities, and lattice thermal conductivity via an iterative solution to the linearized Boltzmann Transport Equation (BTE). We find that despite a very similar atomic structure, D-graphene possesses significantly different thermal properties than that of pristine graphene. At room temperature the calculated thermal conductivity of D-graphene is 600 Wm-1K-1 compared to 3000 Wm-1K-1 for graphene. The out of plane acoustic (ZA) mode contribution decreases from 84% in graphene to 47% in D-graphene. We also reportattribute these distinct properties to the presence of three naturally occurring, low frequency optical phonon modes that possess characteristics of phonon coherence and arise from a folding of the acoustic modes and the associated frequency gap opening, a phenomenon also found in superlattices where an out of plane periodicity is introduced. The optical modes make a significant contribution to the thermal conductivity due to enhanced dispersion, comprising over 18% of the thermal conductivity, while the three coherent branches contribute 9% of the total conductivity. The construction of the D-graphene unit cell presents a new method with which the thermal conductivity of 2D materials can be reduced without making drastic changes to its fundamental composition and demonstrates the potential of using coherent phonon effects to significantly modify thermal transport. This work is supported by a Department of Energy Early Career Research Program under award number DE-SC0019244.