  We study monodromy groups of Picard-Fuchs operators of one-parameter families
of Calabi-Yau threefolds without a point of Maximal Unipotent Monodromy
(\emph{orphan operators}). We construct rational symplectic bases for the
monodromy action for all orphan double octic Picard-Fuchs operators of order
$4$. As a consequence we show that monodromy groups of all double octic orphan
operators are dense in $\mathrm{Sp(4,\mathbb{Z})}$ and identify maximally
unipotent elements in all of them, except one. Finally, we prove that the
monodromy group of one of these orphan operators is arithmetic.
