Finding groups for these dungeons might be very hard until May 15th since the Saga Server is sucking up all the players right now.
The class system in AoC works different than it does in other MMOs, you got the 4 archetypes that define what kind of character you play, Priests will always need to heal, Soldiers will always need to tank (well in 95% of all cases) and Mages / Rogues are there for DPS (in HM dungeons they get additional tasks to fulfill while DPSing). Playing a Conq purely as DPS is “wrong” when you want to do group stuff, as some people already said: You normally always need 2 tanks, 2 healers and 2 DPS, adding a 3rd tank will make the loot distribution harder than it needs to be especially for tanks since all 3 soldier classes roll on the same items whereas only 2 of the 3 healer classes need the same gear in HM dungeons. Adding the “moral factor” to that you get to the point : “you don’t tank therefore you don’t deserve tank items” - and I kind of agree with that since as a DPS player you don’t need tank gear but it’s also very bad rolling on barb gear while barbs can only use one set of armor (well, in most cases).
When forming a group you can make an “agreement” that you would like to have certain items if they drop so they pass on them if they agree with that, many people have better gear on Crom anyways and if they are “only” the blue items they are mostly useless for a lot of people anyways.
However if you want the special epic items it will be a lot harder to get these “for free”, like wanting wisdom rings as DT in the Slithering Chaos dungeon while having a PoM and a ToS in your group, they will most likely leave the group and you wont quickly find new healers that agree with you rolling on them as a DT.
You wont really find lots of groups as DPS conq, you should try tanking, even as offtank where you don’t need to do the main job but still need to be active to switch aggro in risky situations.
I see this misconception (especially) in RF far too often: “I signed in as DPS so I can’t tank!” - that’s not how it works, if I sign in as DPS while playing a ToS, does that mean I am unable to use my healing spells?