How many geometric progressions are possible containing 27, 8 and 12 as three of its/their terms

How many geometrical isomers are possible for

How many geometrical isomers are possible for

Does there exist a geometric progression containing 27,8 and 12 as three of its term ? If it exists, then how many such progressions are possible ?

How many geometrical isomer of (X) is possible ?

How many geometrical isomer of (A) is possible?

There are infinite geometric progressions of for which 27,8 and 12 are three of its terms (not necessarily consecutive). Statement 2: Given terms are integers.