Groups of order 14

There are, up to isomorphism, two groups of order 14, indicated in the table below:

That these are the only two possibilities can be shown via the classification of groups of order a product of two distinct primes. Since $$14 = 7 \cdot 2$$ and $$2 \mid (7 - 1)$$, the number $$14$$ falls in the two isomorphism classes case in that classification.