Quiz:Subgroup structure of symmetric group:S3

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See subgroup structure of symmetric group:S3 for background information.

Basic stuff

Summary table on the structure of subgroups: [SHOW MORE]


View the lattice of subgroups as a picture: [SHOW MORE]

1 What are the possible orders of subgroups of the symmetric group of degree three?

1 and 6 only
1, 2, and 6 only
1, 3, and 6 only
1, 2, 3, and 6 only
1, 4, and 6 only
1, 2, 3, 4, 5, and 6 only

2 What are the possible orders of normal subgroups of the symmetric group of degree three?

1 and 6 only
1, 2, and 6 only
1, 3, and 6 only
1, 2, 3, and 6 only
1, 4, and 6 only
1, 2, 3, 4, 5, and 6 only

3 What are the possible orders of quotient groups of the symmetric group of degree three?

1 and 6 only
1, 2, and 6 only
1, 3, and 6 only
1, 2, 3, and 6 only
1, 4, and 6 only
1, 2, 3, 4, 5, and 6 only