There are at least three types of augmented sixths commonly named the Italian, French, and German augmented sixth chords. These chords are generally used to reach the dominant when performing 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 should also be altered so that it will have the same alterations as in the minor key. Therefore, the chord is said to have been borrowed from the minor key. This applies also to the other chords of the augmented sixth and to the Neapolitan Sixth.
The French sixth is formed on the second degree. It is a seventh chord. Most commonly, it stands in its second inversion. Its third is raised in order to build an augmented sixth interval with the bass:
French Sixth, A Minor
French Sixth, A major
The German sixth chord is built on the fourth degree. It is a seventh chord. It is most commonly in the first inversion. Its root is raised in order 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.