# Calculate order, subgroups and normal subgroups

Given the group $$G= \langle (1,3,6,7,4,2,5),(1,2,3)(4,5,7) \rangle$$.
How do i calculate the order of the group, the subgroups and normal subgroups?
The order is the number of elements. We have the elements 1-7. But is it that easy that $$|G|=7$$?
I hope you can help me.

The conjugate $$(6742513)^{(123)(457)} = (6742513)^2$$. Hence the group is $$\langle (6742513)\rangle:\langle (123)(457)\rangle\cong\mathbb{Z}_7:\mathbb{Z}_3$$, a semi-direct product.