About C7/G — uncommon voicings
C7/G is G, C, E and Bb.
It sounds the same dominant over a still bass. Written as a slash chord rather than an inversion because the point is the bass sitting still underneath.
Dominant over a pedal — the harmony moves, the bass does not.
Also written C7 over G or C7 with G in the bass.
What these less common shapes are
How to use C7/G
In which keys. Every note of C7/G belongs to D minor (the ♭VII) and F major (the V, the dominant).
What to play over C7/G
Every note of C7/G is in C mixolydian, C lydian dominant and C half-whole diminished.
Each of those is a page: the scale across the neck, and the chords it harmonises into — which is where C7/G sits in it. Every scale.
Chords near C7/G
Change one note of C7/G and you have (drop the flat seventh), (the flat seventh becomes the major seventh), (the major third becomes the minor third), (the flat seventh becomes the ninth), (the flat seventh becomes the sixth) or (the major third becomes the fourth).
C7/G is a slash chord — a triad over a named bass note. Slash chords on every root.
The common shapes and the derived voicings come from different places, and both are explained in how this site is built.