Groups of order 20160

Factorization and useful forms
The number 20160 has the prime factorization:

$$\! 20160 = 2^6 \cdot 3^2 \cdot 5^1 \cdot 7^1 = 64 \cdot 9 \cdot 5 \cdot 7$$

Other expressions for this number are:

$$\! 20160 = 8!/2 = (2^4 - 1)(2^4 - 2)(2^4 - 2^2)(2^4 - 2^3) = (4^3 - 1)(4^3 - 4)(4^3 - 4^2)/(3(4 - 1)) = (5^3 - 5)(7^3 - 7)/2 = (4^3 - 4)(7^3 - 7) = 5!(7^3 - 7)/2$$

Group counts
All groups of this order have not yet been classified. The information below is therefore partial.