Not exactly. The Lutherans aren't a subset of the Baptists, or vice versa. But the Amish are Mennonites. I would guess that "Amish-Mennonite" is something like "Judeo-Christian," suggesting a certain amount of commonality. Where I went to school, there was a large community of Old Order Mennonites. They and the Amish have significant similarities, notably plain dress, Pennsylvania German, being very selective of the technology they will allow in the community, and so forth. But there are also significant differences: for example, the Old Order Mennonites have purpose-built meeting houses for church, while the Amish meet in homes. They're different enough that they wouldn't be comfortable living in each other's communities.