I have downloaded an article of A.D. Wallace named The Structure of Topological Semigroups, https://projecteuclid.org/euclid.bams/1183519418.
Theorem 2.1 in the text reads:
"Each subgroup of $S$ is contained in a maximal such and no two of these intersect."
I do not understand what this sentence means, probably because it is missing some words. Can you comment please?