Group theory – Product of the inner garland.

The standard definition of internal semidirect product says that $ G $ is a semi-direct product of $ K $ Y $ H $ Yes $ G = KH $, for some subgroup $ K $ Y $ H $ of $ G $ such that $ K $ It is normal and $ K cap H = {H } $.

Generally garland product of groups. $ K wr H $ It is defined as and external semidirect product with $ K ^ n rtimes_ Phi H $, where $ Phi $ it is a homomorphism $ H a Aut (K ^ n) $.

Is it possible to define an inner crown product without talking about homomorphism, that is, simply decomposing a group into some subgroups that satisfy some conditions?