How is working for a corporation-backed startup like?

What's it like working in a "startup" that's a decade old and with a large corporation as a parent company? This specific one I'm looking at has like 150 employees, not sure if they're profitable.

Based on experience working in startups, I like the flexibility in hours and lax dress code, don't care but don't mind having stock options, and can put up with certain ways of working like 1-2 week sprints, agile...

But have also learned that I prefer a more "big monolith" culture - established processes, defined "SiLoEd" roles where you don't have to be the all-in-one handyman and job/paycheck stability (even at the cost of repeating the same formula of doing work over and over).

Sadly, the only startups that seem to offer that combination are profitable ones - seems like venture-backed, not-yet-profitable or acquired startups only offer chaos and last minute work.

Do startups with big corp parent companies come anywhere close or can they still be chaotic?