Praise be to Allah.
A woman does not have to go for Hajj unless she is able, and having a Mahram who can accompany her is one of the prerequisites for her to be able to go to Hajj. If it is not easy for her to find a Mahram to go for Hajj with her, then she is not able according to Shareeah, because in Islam a woman is forbidden to travel without a Mahram. Therefore Hajj is not obligatory for you unless you find a Mahram. So have patience until Allaah makes it easy for you to have a Mahram with whom you can go for Hajj. You have a valid excuse and there is no sin on you for this. As for going with a group without a Mahram, this is not permissible because of the hadeeth narrated by Ibn Abbaas (may Allaah be pleased with him) who said: The Prophet (peace and blessings of Allaah be upon him) said: No woman should travel except with a Mahram, and no man should enter upon a woman unless her Mahram is with her. A man said, O Messenger of Allaah, I want to go out with such-and-such an army and my wife wants to go to Hajj. He said, Go to Hajj with her.(Reported by al-Bukhaari, 1729). The pilgrims used to go out from Madeenah in one caravan like a group but still the Prophet (peace and blessings of Allaah be upon him) did not allow women to travel without a Mahram.
And Allaah knows best.