Here's another concern regarding your request: It sounds like what you desire is the ability of subgroup non-members to post to the subgroup, but not read messages in it. (Because if you also allowed them to read messages in it, then what is the point of having the subgroup and keeping them out?)
And if that's what you want, then the subgroup accomplishes only letting subgroup non-members to send one message to the board. It does not allow them to participate in a back-and-forth conversation with the board, because they would not be privy to the responses within that conversation.
And if THAT'S true, then the suggestion broached here of making the board members main-group moderators with limited permissions accomplishes exactly what you want.
Messages are the sole opinion of the author, especially the fishy ones.