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Topology

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Moderate

Counting Normal Subgroups

TOPO-VEYPZ9

How many normal subgroups does:

$$D_3:=\langle r,s\mid r^3=s^2=1,rsr=s\rangle$$

...the group of symmetries of an equilateral triangle, have?

Here, $r$ represents rotation by 120 degrees and $s$ represents reflection across a fixed diagonal.

A

$1$

B

$2$

C

$3$

D

$4$

E

$5$