There are at least three types of augmented sixth chords, commonly referred to as Italian, French, and German augmented sixth chords. These chords are generally used to reach the dominant when playing a cadence in major and minor keys.
Italian Sixth, A minor
Italian Sixth, A major
Note: In the case of major keys, the third of the chord must also be changed so that it has the same alterations as in the minor key. Therefore, the chord is said to be borrowed from the minor key. This also applies to the other chords of the augmented sixth and the Neapolitan sixth.
French Sixth, A Minor
French Sixth, A major
The German sixth chord is based on the fourth degree. It is a seventh chord. It is most often found in the first inversion. Its root is raised to create an augmented sixth interval with the bass:
German Sixth, A minor
To learn more about augmented sixth chords click here.
See C > Chord for related entries.