The crystal structures of K-doped K-LTA below and above the Curie temperature of 8 K were analyzed by neutron powder diffraction on the basis of space group F23. We found alternate ordering of Si and Al in a distorted framework and different K clusters in two kinds of alpha-cages. Additional K+ ions are distributed mainly in four- and eight-membered rings of the framework and partially occupy the center of an alpha-cage. K+ ions near the center of a six-membered ring form two kinds of tetrahedral assemblies occupied statistically. Our structural data suggest that the K clusters in the adjacent alpha-cages have different magnetic moments. This is consistent with a spontaneous magnetic moment, which is observable even if the K clusters interact antiferromagnetically.