Both are conventionally united as infraclasses within the subclass Theria (Parker and Haswell, 1897), which contains all living mammals except monotremes.
It was described as Spongilla sceptroides by Scottish-born Australian zoologist William A. Haswell in 1883, who discovered it growing on submerged wood in a pond in the vicinity of Brisbane.
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William Aitcheson Haswell arrived in Australia in 1878, and began working in a marine zoology laboratory at Watsons Bay.