Hyperbolic realization conjecture for knot symmetry types

Let $G$ be a finite cyclic or dihedral group. A $G$-symmetry type of a prime knot is a symmetry type arising from an action of $G$ on the knot. Hyperbolic realization conjecture. For each $G$-symmetry type of a prime knot, there is a $G$-symmetric hyperbolic knot $K$ with that type and for which $G$ is the full symmetry group of $K$. The theorem preceding this conjecture establishes realization for nontrivial knots, and for prime knots except for the listed exceptional types; the conjecture asks for hyperbolic representatives with no additional symmetries.