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I have three 3rd cousins on my mother's side with 66.1-71 cM shared between us. One is male and 2 female. These 3 cousins are 2nd cousins to each other and I believe I am their third cousin. They each have a great grandparent that are siblings, the females have a male great grandparent and the male has a female great grandparent all having the same parents. I am looking for my mother's great grandmother and believe she is in this family.
Where would she fit?
Second cousins share one set of great grandparents. They would each have one grandparent who is the sibling of the other cousin's grandparents. If they are 2nd cousins as you say (and your saying their great grandparents are siblings was in error), and if you are actually the 3rd cousin of each of them, this means that your great grandparent was the sibling of one of their great grandparents.
If all the above is accurate, then your mother's grandparent is the sibling of those cousins' great grandparent.
Your mother's great grandmother (if that is the correct line) would be the great great grandmother of these cousins. This means that you would share one set of 2nd great grandparents with these cousins.
Of course that all assumes that you're really 3rd cousins to them (and that they're really all 2nd cousins to each other). According to the Shared cM Project, your DNA results are well within the range for 3rd cousin.
They are also within the range for:
And many more variations. Check out the chart.
You're on the right track and the DNA evidence does seem to point to you being related to them through the great grandparents they share (triangulate your DNA results to be sure...upload to Gedmatch.com for that). It's just too early to tell the exact relationship. Getting your mom's DNA would help. Ultimately though, it's up to the paper trail.
