These Orders are NOT appendant bodies within Swedish Freemasonry but entirely separate Orders.
They all have degree systems.
Not all of them where founded in Sweden.
Svarta Örns Orden (Order of the Black Eagle).Founded to protect protestants. The Black Eagle was a ship.
W6. Founded 1851 in my hometown, Gothenburg. Has lodges all over Sweden but not outside.
WF. Founded 1865 in Stockholm and has lodges in many cities.
Bifrostorden (The Order of Bifrost, the rainbow bridge of Norse mythology). Founded 1925 in Örebro and has lodges in several cities.
Bifrosrorden works in 10 degrees (last one honorary): I:Freedom, II:Friendship:III:Knowledge,IV:Hope, V:Fidelety,VI:Love,VIITruth,VIIIBeauty,IXWisdomX:? (X can only be held by 30 brothers)
Götiska Förbundet (The Geatish Society). Founded 1815 and has its seat in Gothenburg. It works 6 degrees.
The seat of Götiska Förbundet in Skansen Lejonet , a fortification i have been in and passed many times.
Svea Orden (Order of the Swedes). Founded 1795. Like Götiska furbundet for the Geats (Götaland), Svea Orden works for the understanding of the history of the Swedes (Svealand)
The jewel of Riksgraden (The Degree of the Realm),Götiska Förbundet and Svea Orden shares their highest degree.
Medieval Maritime Order from the Mediteranian, now only working in Sweden and Finland
Svenska Druid Orden (Swedish Order of Druids). Branch of an Order founded in London 1781
Members of Sirius Orden (The Order of Sirius) at a festivity.
There are many , many more Orders active in Sweden but the list would be insane even without pictures.