Step 1: Understand the question.
We must place the class Sphenopsida into its correct plant division.
Step 2: Recall the pteridophyte classes.
Division Pteridophyta is split into Psilopsida, Lycopsida, Sphenopsida, and Pteropsida.
Step 3: Identify Sphenopsida.
Sphenopsida are the horsetails, like Equisetum, with jointed stems and whorled microphyllous leaves. So Sphenopsida sits inside pteridophytes.
Step 4: Reject bryophytes.
Bryophytes are non-vascular and include liverworts, hornworts, and mosses, not Sphenopsida.
Step 5: Reject angiosperms.
Angiosperms are flowering plants with enclosed seeds, divided into monocots and dicots, so they do not contain Sphenopsida.
Step 6: Reject gymnosperms and conclude.
Gymnosperms are naked-seeded plants like cycads and conifers. Therefore Sphenopsida belongs to pteridophytes.
\[ \boxed{\text{pteridophytes}} \]