It dealt with science masquerading as religion which was totalitarian and the rebels used witches and the occult to defy them and fight for freedom. The "Great God" scientifically produced miracles.
I read this book years ago.
This review on Goodreads mentions the Great God and the witches:
Three hundred years after a nuclear holocaust, humanity is ruled by a secretive religious brotherhood, the Hierarchy of the Great God, which uses science as the supernatural means of ensuring its control over an impoverished, predominantly illiterate population. Opposing this brotherhood is a secret society of witches, the followers of Sathanas, seeking to use science to overthrow the brotherhood's tyrannical theocracy. A young Hierarchy priest, Brother Armon Jarles, skeptical of his beliefs and the Hierarchy's orthodoxy, soon finds himself caught in the bitter struggle between both groups. A struggle that is meant to gather darkness against the Hierarchy's grip on power.
Another review mentions the "Great God" producing miracles:
Written in the 1940's this novel postulates a future where the Hierarchy control the populace by using religion as a control. Using science to produce false "miracles" the Hierarchy brainwashes the populace into obedience--the more clever of the 'commoners' are encouraged to join the priesthood.
So, when an group of revolutionaries begins to overthrow the tyrants, the rebels disguise themselves as "witches" and use their science to create miraculous effects ascribed to "Sathanas".
Found with the Google query
book science religion "great god" "rebels" site:goodreads.com which returned the Goodreads page, highlighting the second review.