If we add a half hexagon to a tetrahex we get 150 pieces seen here in three congruent shapes.
If we remove the piece with a hole the remaining 149 pieces form the figure below.
A number of sliced parallelograms are also possible.
Of the 296 one-sided pieces 294 have no hole. These are shown here in seven 7x27 parallelograms. The lower diagram shows a set of constructions which can make three parallelograms of three 'rectangles'.