  We address a question of Cavenagh and Wanless asking: which finite abelian
groups arise as the canonical group of a spherical latin bitrade? We prove the
existence of an infinite family of finite abelian groups that do not arise as
canonical groups of spherical latin bitrades. Using a connection between
abelian sandpile groups of digraphs underlying directed Eulerian spherical
embeddings, we go on to provide several, general, families of finite abelian
groups that do arise as canonical groups. These families include: any abelian
group in which each component of the Smith Normal Form has composite order; any
abelian 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 rank
two.
