We studied double superconducting (SC) domes in LaFeAsO(1-x)H(x) by using 75As and 1H nuclear-magnetic-resonance techniques and unexpectedly discovered that a new antiferromagnetic (AF) phase follows the double SC domes on further H doping, forming a symmetric alignment of AF and SC phases in the electronic phase diagram. We demonstrated that the new AF ordering originates from the nesting between electron pockets, unlike the nesting between electron and hole pockets, as seen in the majority of undoped pnictides. The new AF ordering is derived from the features common to high-Tc pnictides; however, it has not been reported so far for other high-Tc pnictides because of their poor electron doping capability.