Diwan's subdivision conjecture for planar maximal 3-degenerate graphs

Let $H$ be a planar maximal 3-degenerate graph. A subdivision of $H$ is a graph obtained by replacing edges by internally vertex-disjoint paths. Diwan's conjecture. Every graph with minimum degree at least $|V(H)|-1$ contains a subdivision of $H$. The conjecture would imply the proposed apex-outerplanar minor conjecture; it remains open.