Yes. Annex III Class I point 12 covers routers, modems intended for the connection to the internet, and switches. A home or office router is an important product with digital elements.
Routers, modems intended for the connection to the internet, and switches
Annex III, Class I, point 12, Regulation (EU) 2024/2847
The modem half carries a qualifier the other two do not: intended for the connection to the internet. A modem for a closed industrial link is a different reading from a cable modem.
Point 6 is the management system, point 12 is the hardware. Both are Class I, so the conformity route is identical - but they are different lines of the annex and a report should cite the one that applies.
Point 10 attaches a host to a network; point 12 connects networks to each other.
The same rulebook that produced this page runs the free check. It reads your products, classifies each one against Annex III and IV, and gives you an indicative verdict with the reasoning and citation for every product.
Indicative assessment - not legal advice and not a conformity assessment.