There are as many possible minor chords as there are major chords. A minor chord can be created simply by flattening the third degree (middle note in a root position chord) of any major chord. E.g, an F chord contains the notes F, A and C. To create an F minor chord, you simply flatten the third (A becomes Ab).
To create a G minor chord, you take a G major chord (G B D) and once again flatten the third (B becomes Bb), etc. Once you have the basic minor chord, it can be arranged into root position, first inversion and second inversion. The following example demonstrates these inversions for the chords Fm and Gm.
Here are some examples which make use of these inversions.