[RavenSplat]

For most of the 23rd Century Starfleet used a badge (shown below) to mark one of it's 4 main divisions with a red uniform (apart from a brief stint in the 2250's were bronze was used), and used yellow in the 24th century and beyond.
However I have found it that unlike the other Divisions of Command, Science and Medical the final main division is referred to with many names due to the many different departments and roles it contains.

So what I am wondering is when you see that badge or uniform on a random crew member what is the first job that you think they do and what you.
I would also like to know what you call this Division and how you refer to the uniform worn by it's members.

If the responses are interesting and varied enough I may follow this up with a series of polls with the answers given here.
Also please don't use Memory Alpha or anything I want to hear your opinion not the true answer here.

[Heyallo]

Operations/Engineering

[Petrarch]

It's always been Operations to my eye, which includes Engineering, Ops and Security.

Also this:

[Solace]

Operations/engineering, I quite like that simplistic chevron design though!

[Vox]

Ops/Engineering

[Novalance]

That symbol is also used in-game in STO for the engineering team power So my immediate go to is Engineering

[RavenSplat]

It's always been Operations to my eye, which includes Engineering, Ops and Security.

Also this:

That is certainly another option for them. Expendable is also pretty accurate espeically for TOS

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That symbol is also used in-game in STO for the engineering team power So my immediate go to is Engineering

I do find it interesting that Tactical got the command insignia and colours in STO. Does lead to a bit of Engineering bias in what the insignia represents to most people.

[Sunfire]

Engineering for me, too.

[Chris Wilkinson]

I consider it operations/engineering/security for that era

[WelshAvenger]

I always believed that the division was Operations which contained Security/Engineering/Communications departments.
Weirdly though, in TOS Bones always wore the Science insignia unless he was wearing the short sleeved shirt which had a Medical cross emblem, whereas the few images I can find for TOS M'Benga had him in a short sleeve shirt with the Science insignia.

[darthnovawave]

I've always seen it associated with engineering/operations. That said, the various showrunners have hardly shown the attention to detail that many fans have shown when it comes to costume details (for instance, the Lower Decks jab at rank pips being due to stray corn kernels because of people not wearing the same number of pips each episode). Thus, it wouldn't surprise me to see examples of the division insignias being inconsistent too. I don't think there has been an in-show callout of these logos either, so we are probably one script away from those icons being retconned to some other meaning at any given time.

[RavenSplat]

I always believed that the division was Operations which contained Security/Engineering/Communications departments.
Weirdly though, in TOS Bones always wore the Science insignia unless he was wearing the short sleeved shirt which had a Medical cross emblem, whereas the few images I can find for TOS M'Benga had him in a short sleeve shirt with the Science insignia.

It is Operations but how much it covers does change from time to time. Like sometimes it covers bridge officers like sensor personal and helms-people and other times they get thrown in Command.

Whether Medical is it's own Division does seem to change from show to show. Like Disco, SNW and sometimes TOS have the separate uniform and badge while DS9, Voy and TNG and the shows set after like Picard and Lower decks regard it as a branch of sciences. Never is consistent with that one but I like to count it as a separate one because half of medical went to Medical school and then a quick version of the Academy rather than full Academy training of a Science officer so I can't see how they would be counted as the same in the system.

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I've always seen it associated with engineering/operations. That said, the various showrunners have hardly shown the attention to detail that many fans have shown when it comes to costume details (for instance, the Lower Decks jab at rank pips being due to stray corn kernels because of people not wearing the same number of pips each episode). Thus, it wouldn't surprise me to see examples of the division insignias being inconsistent too. I don't think there has been an in-show callout of these logos either, so we are probably one script away from those icons being retconned to some other meaning at any given time.

It certainly isn't consistent. For example Helms personal are sometimes Operation (Data and Detmer all come to mind here) while others are Command (Sulu, Travis Mayweather, Boimler and Tom Paris). I do wonder just how much they would want to retcon at this point though, outside of maybe the different ships having different badges in TOS, because of all the fans who pay far too much attention to this stuff.

[darthnovawave]

It certainly isn't consistent. For example Helms personal are sometimes Operation (Data and Detmer all come to mind here) while others are Command (Sulu, Travis Mayweather, Boimler and Tom Paris). I do wonder just how much they would want to retcon at this point though, outside of maybe the different ships having different badges in TOS, because of all the fans who pay far too much attention to this stuff.

Large organizations in real life often "restructure" to realign different groups in hopes that somehow they'll stumble upon some "magical" combination that will work better than what they have today. In practice it rarely if ever works since such changes create both benefits and new problems of their own. Apparently hundreds of years from now and people apparently still fall for that trap, at least at Starfleet. I blame their terrible screening process for promoting people to admiralty positions.

[ThatOneGuy1191]

To me, it always - and still does - mean that if they have that badge, and they're not Scotty or Uhura, then they're not going to be in another episode.