Ishmael has the right of inheritance by the law of primogeniture- much like Israel in relation to the Gentiles. He has rights under the law. He is nevertheless rejected for the child of the promise. He is exiled twice and the second time permanently- like Israel. We are told that he oppresses Isaac and is exiled for it- much like Israel's persecution Christ and the Church.
Isaac is born by a miracle like Christ. He is persecuted like by his older brother, like Christ by Israel and the Church by its "older brother" so to speak. He is elected though he does not have that right via the law- like the NT Church. Finally, he goes to his death and is "resurrected"- like Christ. On the other hand, a substitute (the Ram) is offer for him- again, like the Church.
This is, I think, rather remarkable and I think it goes a long way to showing that Paul's allegory is not merely illustrative or far fetched as some interpreters suggest it is.