Physical Remoteness is Not Going to Work
With the tech of today, and for any society more than a few dozen people, it is not possible.
Living underground or under the ocean or under Antarctic ice is simply not going to fly with today's tech. It is possible to live in those places, but it would be a major undertaking that is simply not possible to do it unobserved.
Consider that you would want a power source. Consider what you would need to stay alive under ice. You need heat, and protection from the ice. You could build steel reinforced walls that would resist crushing. Then provide heat, light, greenhouse food, and such. But for more than a very small number of people this would be quite obvious. You would need to either create these items on-location, or ship them in.
Shipping thousands of tons of stuff to Antarctica is going to get noticed. Setting up a factory is going to get noticed. If for no other reason than you would be spewing out CO2 where none had been released previously.
So, unless you are prepared to limit your group to about ten people, it will physically get noticed pretty much anywhere you put it.
Secret Society
Secret societies are a challenge. There are lots of social groups that have tried to stay secret. But we know about them. If you have more than a few people moving in a larger culture, there will be people who spill the secret. It would take quite extraordinary methods to keep such a secret if your group was, say, thousands of people or more.
Even having a combination of physical remoteness and a secret society is highly unstable. The deepest secrets of such folk as The Mormons or The Masons are available on line and in parody musicals. When a group is more than a few people, people will leave and take those secrets with them.
One imagines a town "in the wilderness" where everybody is a member of The Club. Then some ordinary disagreement arises. 199
Some couple has a rancorous breakup and one of them storms off to parts far-far-away to get away from the ex. And then he is outside the safety of the town. And wants to form new relationships with people outside The Club. And every day he has temptation to spill the secret for a variety of psychological and social reasons. This has happened for many groups.
Non-Humans
Suppose your secret folk are, in some manner, much smaller.
Another answer already suggested that they might be small enough to live on a grain of rice. It would require quite radically different biology to what we experience. Organisms that small cannot be as smart as humans if they are based on DNA-carbon type life cycles. There is not enough room and there is not enough energy. But if they were aliens, who knows?
Consider a VR device that occupies some such space as a football-field sized area. It could easily be added to an underground layer under some mundane structure such as a parking lot. The servers could be secretly diverted from a number of mundane projects. Say, every time Amazon or Google sets up a local server farm, 10 or 20 servers walk out the back of the facility. Provide some electricity, and maybe some air flow for cooling, and your entire society is on-line. They might have an internet connection that allowed them to sell intellectual property such as stories, engineering designs, etc.
They would need a very small number of human assistants to keep things going. Maybe one family that owns the land the VR rig is under. They could handle things like being the literary agents for the IP produced. And keeping that parking lot from being excavated. Because their income depends on the secret staying secret, there is a possibility it could be stable. 159