The Netgear WNDR3400v3 uses a somewhat simple HTTPS basic authentication protocol for remote login requests (should be the same for local, but with HTTP), but checks for a session cookie (if the current session cookie is not still valid). To authenticate to the router, first send a request to the root of the router, save the cookies (this will 401), and then use said cookie to get whatever page you would like.
wget --keep-session-cookies --save-cookies cookies.txt -O cookies.html https:///ROUTER_IP:ROUTER_PORT --no-check-certificate \
(if that command doesn't give you a cookie, try using these headers, replacing YOUR_AUTH with a base64 ascii encoded string containing "YOUR_USERNAME:YOUR_PASSWORD")
{
"Host": "YOUR_IP:YOUR_PORT",