English syllables can start with a cluster of up to three consonants and end with a cluster of up to four (but rarely do). It follows that two adjacent syllables (less likely in the middle of one word, more likely between two words) can conglomerate a cluster of up to seven consonants (but rarely do). Clusters of six or five consonants are not uncommon. This morning’s anthem contained the cluster /mftgl/ (or really /mft.gl/) in the sentence ‘Sing ye to the Lord, for he has triu*mphed gl*oriously’.
It is possible to construct a sentence which conglomerates a seven-consonant cluster across two words. There is a Sherlock Holmes story in which Holmes deduces someone (?Watson/a client)’s life story by examining his pocket watch. Part of his deduction was based on the fact that he gli*mpsed scr*atches around the hole into which the winding key was inserted.