Have you checked the option to share the map with everyone? Still, if you are not able to embed the map for public, you could use the shortened URL to share the map with people outside the organization?
Although you are sharing this map with everyone, copy and use the shortened URL link on this dialog to allow people outside your organization to view the map.
In the Embed HTML code, you could try replacing the src parameter (inside double quotes) with the shortened URL.
Think Location
