The 'Cronquist System' of flowering plant classification groups flowering plants (Magnoliophyta) into two classes (monocots and dicots) with related orders (groups of families) placed in subclasses. (see Arthur Cronquist, 1988 The Evolution and Classification of Flowering Plants).
The 'Takhtajan System' of flowering plant classification treats flowering plants as a division or phylum (Magnoliophyta) with two classes (monocots and dicots) which are organized into subclasses. Higher level organization is similar to the Cronquist System, but a bit more complex. Takhtajan uses the superorder as the basic unit of the subclass and this pattern of organization is also used in the Thorne System of flowering plant classification (see Armen Takhtajan, 1997, Diversity and Classification of Flowering Plants).
Thorne treats the flowering plants at the rank of class with an initial bifurcation into two subclasses. Related orders are placed within each subclass as superorders and, within these, clusters of related families are grouped into suborders. There is detailed classification (subfamilies, tribes) for larger families.