What might the statue of neptune symbolize in robert browning’s “ my last duchess”?

It represents the hierarchical dominance of men over women in Victorian society.

Robert Browning's poem My Last Duchess is written in a poetic style known as 'dramatic monologue' in which the readers infers most of what's knowable through the speaker's own words.

The poem portrays a Duke entertaining an envoy from a Count who's daughter the Duke intends to marry. The Duke also implies he had his last wife, the duchess, killed.  That he points to a statue of Neptune, (the Greek god of the sea wrestling a seahorse) in the very last few lines of the poem seems to act as a counter point to the painting of his wife which he just showed to the envoy shortly before insinuating he had her killed. The implicit message seems quite obvious: the dominant Duke is willing to wrestle and control his female companions in a similar fashion than Neptune does with the seahorse.

Over the course of the poem, the Duke reveals his obsession with control. The statue of Neptune taming a seahorse symbolizes the Duke’s persona.

The Duke boasts of his aggression toward his dead wife in an effort to gain complete mastery over her most simple pleasures. His reference to the statue of Neptune emphasizes his hunger for mastery over all of the things around him.

Just like the painting of his wife, which has become the symbol of complete submission to the Duke’s will, the statue is a symbol of captivity. The statue is an image of the seahorse being subdued to the will of Neptune. The Duke also wants to subdue others to his will.

(PLATO)