# 3rd Isomorphism Theorem

This 3rd Isomorphism Theorem can be intuitively understood as:

G partitioned by a bigger normal subgroup H
is isomorphic to:
{G partitioned by a smaller normal subgroup K (which is a subgroup of H)}
partitioned by
{H partitioned by a smaller normal subgroup K}

or, by ‘abuse of arithmetic’: divide G & H by a common factor K.

$(G / H ) = (G / K ) / (H / K )$

Analogy:
\$100 / \$50 = 2 (two \$50 notes makes \$100)
is same (isomorphic) as
\$100 / \$10 = 10, (ten \$10 notes makes \$100)
\$50/\$10 = 5, (five \$10 notes makes \$50)
then 10/5 = 2 (ten notes split into five is two )