The female subduing the dragon represents humanity taming its wilder instincts and channeling them to useful purpose. Unlike St. George who merely killed his dragon, she tames hers and gains its respect, adding its strengths to her own and becoming invincible. She is related to Artemis, or Diana the Huntress, and other pagan Queens of the Beasts.
Strength reversed reveals wasted effort, failure, and the possible alienation of others through the abuse of power. In the reversed card the dragon has won the battle and the woman has become tainted by self-interest. By losing sight of any larger goal she loses the sympathy and the support of others. Here, restraint, modesty, and patience are called for.