A transmission for a propulsion system. The propulsion system includes a power unit, a power transfer system, and a propulsion element. The transmission incorporates a summation, a propulsion output, and a power transfer transmission system, which receives power from the power unit and/or the power transfer system of the propulsion system. The power transfer transmission system includes a propulsion output transmission and a summation transmission, where the propulsion output transmission receives power from the summation transmission and directs the power to the propulsion element. The power transfer transmission system provides for transfer of power between the power transfer system and the summation transmission. The power transfer transmission system includes a power transfer shaft and a power transfer coupler and selectively connects the power transfer shaft to a propulsion outlet shaft, such that power is transferred directly from the power transfer system to the propulsion output transmission.