Symmetric group S_6.
(It is made by all the possible permutations of 1,2,...,6. It has 6!=720 elements).

Symmetric group S₈.
(It is made by all the possible permutations of 1,2,...,8. It has 8!=40320 elements).
 

Alternanting group A₆.
(It is made by all the permutations of 1,2,...,6 of even class. It contains 360 elements).

Alternanting group A₇.
(It is made by all the permutations of 1,2,...,7 of even class. It contains 2520 elements).
 
 

Diehedral group D₄.
(It is made by all the symmetries of a square. It contains 8 elements).
 
 

Dihedral group D₇.
(It is made by all the symmetries of a regular ettagon. It contains 14 elements).
 

Dihedral group D₈.
(It is made by all the symmetries of a regular octagon. It contains 16 elements).

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