Groups of order 408

This article gives information about, and links to more details on, groups of order 408
See pages on algebraic structures of order 408 | See pages on groups of a particular order

Statistics at a glance

Factorization and useful forms

The number 408 has prime factors 2, 3, and 17, with prime factorization:

$\!408=2^{3}\cdot 3\cdot 13=8\cdot 3\cdot 17$

Group counts

Quantity	Value	List/comment
Total number of groups up to isomorphism	46
Number of abelian groups (i.e., finite abelian groups) up to isomorphism	3	(number of abelian groups of order $2^{3}$) times (number of abelian groups of order $3^{1}$) times (number of abelian groups of order $17^{1}$) = $3\times 1\times 1=3$. See classification of finite abelian groups and structure theorem for finitely generated abelian groups.