I assume the question used the versatile word "let" to mean the teacher becomes the decision maker by choice, and not by command, which is otherwise rude.
Personally, I would avoid the direct translation. The following suggested expressions use
私のグループは that refers to the group I would be in (translated as "my grouping"); not the literal "my group", which is yet to exist in this context.
A. 私のグループは 先生に決めてもらった｡
A. [I] had [my] teacher decide for my grouping.
B. 私のグループは 先生に決めてもらう方にした｡
B. [I] opt for the choice that [my] teacher would decide for my grouping.
A is the straightforward, passive voice. The phrase
先生にきめてもらった is probably the shortest phrase one can use readily to describe that "the teacher decide (do) the group (X) for me".
B is the alternative expression made by modifying
A, which turns the passive voice to not-so-active voice. As a result,
B would be perceived less straightforward, but would appeal the speaker as slightly independent (on the surface only, because the teacher is still the decision maker by choice).
B will make sense only when "the teacher would decide my grouping" is available as a choice, due to the phrase
〇〇方にした being used to refer "that choice". In contrast,
A will make sense regardless of that is a choice or not.
Then again, these expressions may vary when describing the "do": If the groups were already formed, the teacher would choose (選ぶ) which group the student (I) would be in; else if no groups were formed yet, the teacher would decide (決める) how the groups would be formed, or decide which and which students would be put into the groups.