11. (15 points) As shown in the figure, a regular hexagon with a side length of 3 is divided into 54 small equilateral triangles with a side length of 1 by 3 sets of lines parallel to its sides. How many regular hexagons can be formed with the vertices of these small equilateral triangles?
【Analysis】Observe the figure, count the number of regular hexagons, which can be categorized by counting, such as hexagons with side lengths of 1, side lengths of 2, and side lengths of 3, and then add them up.

【Solution】According to the analysis, the number of regular hexagons with a side length of 1 is: 19;
The number of regular hexagons with a side length of 2 is: 7;
The number of regular hexagons with a side length of 3 is: 1,
In addition, as shown in the figure, the number of two types of regular hexagons is: $7+2=9$.
The total number of regular hexagons is: $19+7+1+9=36$. Therefore, the answer is: 36.