hi! 🐧 mod here! my joseon knowledge is not as great as 🐣 mod, but he is a little sick so i will answer you! there were other positions too, but when you mentioned 6, i remembered about the 6 ministries/ministers that were very high-ranking officials:
ministry of personnel (Ijo): appointment of officials
ministry of taxation (Hojo): taxation, finances, census, agriculture, and land policies
ministry of rites (Yejo): rituals, culture, diplomacy, national civil service examinations
ministry of defense (Byeongjo): military affairs
ministry of justice (Hyeongjo): administration of law, slavery, punishments
ministry of works (Gongjo): industry, public works, manufacturing, mining
[each ministry was called a Yukjo]
now how would the ministers themselves be addressed? their official titles were, if we take minister of personnel, Ijo Panseo. similarly for minister of taxation, his title was Hojo Panseo. Panseo here translates to Minister/Chief Secretary.
sometimes, the honorific Daegam was used as a mark of respect as this honorific is akin to calling someone Your Excellency in english. it wasnt in their title but while lower ranks addressed them they would use it. so it would go something like Hyeongjo Panseo Daegam for minister of justice.
apart from them, there were the 3 state councillors and other high ranking officials.
in the 6 ministries there were further rankings, so if you need those, do send another ask! hope i could help! and please ignore any typos XD