In this case, the main sentence has an embedded clause at the end:
"I think that ’twixt the negroes of the South and the women at the North, all talking about rights, the white men will be in a fix pretty soon." (embedded clause in bold.)
This embedded sentence is complex as it has one independent clause ("...the white men will be in a fix pretty soon.") and a dependent clause ("...that 'twixt the negroes of the South and the women at the North...")
The main sentence presents a simple syntactic pattern: S.V.O. (Subject-Verb-Object), as it contains a mono-transitive verb ("think") which requires a direct object following it ("that..."). The subject of the sentence is the personal pronoun "I". This S.V.O. pattern is present in sentences much simpler, such as "I think this" or "I like that."