Solvability and affinity conjectures for finite superconnected quandles

Let $Q$ be a finite superconnected quandle, meaning a quandle whose displacement group acts transitively on each of its displacement-group orbits. A quandle is solvable if its derived series terminates at the trivial quandle, and it is affine if it is isomorphic to an affine quandle constructed from an abelian group.

Superconnected quandle conjectures.

1. Every finite superconnected quandle is solvable.
2. Every finite simple superconnected quandle is affine.

These conjectures extend the known results for finite latin quandles: finite latin quandles are superconnected and solvable, while finite simple latin quandles are affine. The assertions for arbitrary finite superconnected quandles remain open.