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We address a question of Cavenagh and Wanless asking: which finite abeliangroups arise as the canonical group of a spherical latin bitrade? We prove theexistence of an infinite family of finite abelian groups that do not arise ascanonical groups of spherical latin bitrades. Using a connection betweenabelian sandpile groups of digraphs underlying directed Eulerian sphericalembeddings, we go on to provide several, general, families of finite abeliangroups that do arise as canonical groups. These families include: any abeliangroup in which each component of the Smith Normal Form has composite order; anyabelian group with Smith Normal Form$\mathbb{Z}^{n}_p\oplus\left(\bigoplus_{i=1}^k\mathbb{Z}_{pa_i}\right)$, where$1\leq k$, $2\leq a_1,a_2,\ldots, a_k,p$ and $n\leq 1+2\sum_{i=1}^k(a_i - 1)$;and with one exception and three potential exceptions any abelian group of ranktwo.

On which groups can arise as the canonical group of a spherical latin bitrade