The standard grips this chord is usually shown with.
Caug7 is C, E, G# and Bb, a augmented seventh. The shape this page opens on is written x323x4, lowest string first.

Also written C7#5, C+7 or C7(#5). The same chord either way; which spelling you meet depends on who wrote the chart.
There are 5 common shapes for Caug7 on the guitar, and 25 derived voicings in 4 families.
The common shapes, written lowest string first: x323x4, x36354, 8x8990, 878x9x, x-x-10-13-11-12.
Shell. Root, third and seventh: the guide tones fix the quality, so the fifth is dropped. That is what leaves a string free, so pick a tension to put on top. Caug7 has x3x354, 8x899x.
Drop 2. A close-position chord with the second voice from the top lowered an octave. Sits on four adjacent strings. Caug7 has x1211x, 4323xx, xx6556, 6765xx, xx8998, x-11-10-9-11-x, x-13-14-13-13-x, xx2314.
Drop 3. The third voice from the top lowered an octave. The dropped voice becomes the bass, which is why a string is skipped. Caug7 has 4x231x, x1x110, x3x354, x7x596, 6x655x, x-11-x-9-11-8, 8x899x, 12-x-10-13-11-x.
Open string. An open string left ringing against a fretted grip. Because it costs no finger, it sounds a note the closed shape has none left for -- a tension on top, or a pedal root underneath. Either a familiar grip with open strings added, or a shape so sparse the open strings carry the chord. These belong to their key rather than to a shape, so D, A, G and E have many and Eb a handful. Caug7 has 030354.
Tensions. A shell of Caug7, root, third and seventh, leaves a string free, and the tones that belong over it are the b9 (Db), the 9 (D), the #9 (D#) and the #11 (F#).
The common shapes and the derived voicings come from different places, and both are explained in where the chords and the theory come from.
Shows each chord the way this style would voice it, and marks which of its alternatives belong to the idiom.