Praise be to Allah.
It is permissible for a woman to prompt her mahram if he makes a mistake in the prayer, on condition that there not be any non-mahram men present who could hear her. The prohibition on women saying Subhaan Allaah and the command for them to clap which are mentioned in the hadeeth quoted below apply in situations like that mentioned in the hadeeth, which is where a woman is praying with non-mahram men.
If they are praying with non-mahram men, women should not raise their voices to say Ameen during the prayer or to say Subhaan Allaah to alert the imam to a mistake.
It was narrated from Sahl ibn Sa’d al-Saa’idi that the Messenger of Allaah (peace and blessings of Allaah be upon him) went to Bani ‘Amr ibn ‘Awf to reconcile between them. (In the meantime) the time for prayer came, and the muezzin came to Abu Bakr and said, “Will you lead the people in prayer, and should I say the iqaamah?” He said, “Yes.” So Abu Bakr started to lead the prayer. Then the Messenger of Allaah (peace and blessings of Allaah be upon him) came when the people were still praying, and he passed through the rows until he stood in the first row. The people clapped but Abu Bakr used not to glance sideways whilst he was praying. When the people’s clapping continued, he turned and saw the Messenger of Allaah (peace and blessings of Allaah be upon him). The Messenger of Allaah (peace and blessings of Allaah be upon him) gestured to him to stay where he was, so Abu Bakr (may Allaah be pleased with him) raised his hands and praised Allaah for what the Messenger of Allaah (peace and blessings of Allaah be upon him) had told him to do. Then Abu Bakr stepped back until he was level with the row and the Messenger of Allaah (peace and blessings of Allaah be upon him) came forward and led the rest of the prayer. When he finished he said, “O Abu Bakr, what kept you from staying put when I told you to?” Abu Bakr said, “It was not right for the son of Abu Quhaafah [referring to himself] to lead the Messenger of Allaah (peace and blessings of Allaah be upon him) in prayer.” The Messenger of Allaah (peace and blessings of Allaah be upon him) said, “ Why did you clap so much? If something happens to anyone during his prayer, let him say Subhaan Allaah, for if he says Subhaan Allaah, people will take notice. Clapping is only for women.”
(Narrated by al-Bukhaari, 652; Muslim, 421)
Ibn Hajar said:
He did not let women say Subhaan Allaah because they are commanded to lower their voices in prayer in all circumstances, because of the fear that their voices may cause fitnah (temptation). He forbade men to clap because this is something for women.
Fath al-Baari, 3/77
Ibn ‘Abd al-Barr said:
Some of the scholars said: It is makrooh for woman to say Subhaan-Allaah (in such circumstances) and it is permissible for them to clap because most women’s voices are soft and a woman’s voice may distract the men who are praying with her.
Wali al-Deen al-‘Iraaqi said:
If a woman goes against what is prescribed for her and says Subhaan Allaah for something that alarms her, her prayer is not invalidated, but if she says it quietly in such a manner that no one can hear her, this do not serve the intended purpose. If she says it out loud so that the one whom she wants to make understand can hear it, then what we should say in this case is that if (the imam) is another woman or a mahram, then it is not makrooh, but if (the imam) is a non-mahram man, then it is makrooh and indeed it may be haraam, if we assume that the woman’s voice is ‘awrah.
We do not mean that in such circumstances it is prescribed for her to say Subhaan Allaah, rather we say that if she does say Subhaan Allaah, it is not makrooh; what is prescribed for her and what is better is for her to clap, because the apparent meaning of the Prophet’s words “Clapping is for women” is that it is prescribed in all cases. And Allaah knows best.
Tarh al-Tathreeb, 2/248, 249
Al-Zarkashi said: The scholars prescribed clapping for woman in all circumstances, and undoubtedly this applies when a woman is in the presence of non-mahram men. If she is with women or men who are her mahrams, then she may say Subhaan Allaah, like reciting out loud in their presence.
Mughni al-Muhtaaj, 1/418
And Allaah knows best.