Summary: A non-nilpotent finite group whose proper subgroups are all nilpotent is called a Shmidt group. A subgroup \(A\) is said to be seminormal in a group \(G\) if there exists a subgroup \(B\) such that \(G=AB\) and \(AB_1\) is a proper subgroup of \(G\), for every proper subgroup \(B_1\) of \(B\).
Groups that contain seminormal Shmidt subgroups of even order are considered. In particular, we prove that a finite group is solvable if all Shmidt \(\{2,3\}\)-subgroups and all \(5\)-closed \(\{2,5\}\)-Shmidt subgroups of the group are seminormal; the classification of finite groups is not used in doing so. Examples of groups are furnished which show that no one of the requirements imposed on the groups is unnecessary.