The Kaluza-Klein reduction giving rise to four-dimensional N=4, half-maximal SO(4) gauged supergravity of the D = 11 supergravity is mainly studied. Apart from some special cases, a spherical Kaluza-Klein reduction is in general not consistent. There exists, however, an alternative way to provide a consistent Kaluza-Klein reduction. The guaranteed-consistent reduction, known as the Scherk-Schwarz reduction, requires doing the dimensional reduction on a group manifold of some particular Lie group. From the fact that the SU(2) group manifold is topologically S3 embedded in the S7, the Kaluza-Klein reduction involving S3 can be obtained from a group manifold reduction via replacing the two S3 in the reduction ansatz by the two SU(2) group manifolds. The reduction ansatz is guaranteed to be consistent and give some understanding for the consistency of S7 reduction. By this reduction ansatz, solutions in four-dimensional N=4 SO(4) gauged supergravity theory can be embedded in 11-dimensional supergravity.