Spin liquids, multiferroics, and doubly-chiral helical structures are just some of the exotic magnetic states found in the langasite compounds. A subclass of the langasite group, the Te{sup 6+}-containing dugganites, has also shown exotic magnetism including magnetoelectric coupling, coexisting complex long-ranged ordered structures, and low-field induced magnetic transitions. Here, we present the first detailed structural study of Pb{sub 3}TeMn{sub 3}P{sub 2}O{sub 14} as well as the first neutron scattering measurements. This material undergoes long-range magnetic ordering, similar to the multiferroic Ba{sub 3}NbFe{sub 3}Si{sub 2}O{sub 14}, at T{sub N}=6.6 K, which is consistent with previous magnetization measurements. However unlike any other langasite or dugganite studied to date, we present evidence of a large, pseudohexagonal incommensurate supercell that alters the nuclear and magnetic structures away from the langasite ideal. - Graphical abstract: Two geometrically frustrated cationic substructures of the langasites and dugganites have profound effects on the magnetism of these compounds. In Pb{sub 3}TeMn{sub 3}P{sub 2}O{sub 14}, Mn{sup 2+} (S=5/2) isolated trinuclear units are shown in yellow, while the red distorted kagome network is nonmagnetic. (For interpretation of the references to color the reader is referred to the web version of this article.) Highlights: • Polycrystalline Pb{sub 3}TeMn{sub 3}P{sub 2}O{sub 14} wasmore » prepared. • Found evidence of a large, pseudohexagonal supercell that is incommensurate with the subcell. • Long-range antiferromagnetic ordering is observed below T{sub N}=6.6 K similar to Ba{sub 3}NbFe{sub 3}Si{sub 2}O{sub 14}. • Broken symmetry probably causes magnetic peak splitting in this system.« less