In his papers [4], [5] and [6] Guan-Aun How described some properties of SM (subnormally monomial) groups. He proved that the class of SM groups is the intersection of the class of CSF (chiefly sub-Frobenius) and the class X of those solvable groups G, for which for all primes p and for all subgroups A, Op(A) has no central p-factor. Among other things, he proved that the class of SM-groups is closed under taking direct products, factor groups and subgroups. First we consider the relation between SM groups, subgroup-closed M-groups and supersolvable groups, showing that these classes are all distinct. For the class of Frobenius groups the first two classes coincide, and they properly contain the class of supersolvable Frobenius groups. For Frobenius complements the three classes are equal. The class SM is not closed under extensions. We show that even the split extension of an abelian group with an SM-group can be non-SM. On the basis of the notion of relative M-groups, we introduce the notion of relative SM-groups. We investigate whether some results which are known to be true for relative M-groups, remain true for relative SM-groups or not. Some of them remain true: we show that every SM-group is relative SM with respect to every abelian normal subgroup. According to [7], if G/N is supersolvable, then G is relative M-group with respect to N. The analogous statement is not true for SM: it may happen that G/N is supersolvable, but G is not relative SM with respect to N. However, if G/N is nilpotent, then G is relative SM with respect to N.