As in, block-level organization.
The best ones start off as Neighborhood Watch-type. It can be informal (barbeque buddies shooting the bull, and deciding on organizing to keep an eye on the neighborhood. Those who need to walk a dog are likely recruits; they are out there already, and might as well make themselves useful.
In a SHTF situation, it will really pay off if you know your neighbors, who can be trusted, and – more importantly – who cannot. That information can save your life.
Now, will neighboring groups occasionally interact? Sure. The Block Captains should have a working relationship with nearby groups. They can learn a lot about local government, common problems, and ways to improve life for their own neighborhood.
But, the main focus needs to be on those near to you.