SVT published a list of the active gangs in the Stockholm region. It gets informative when you start to dig around on forums like Zaramis and others. Many groups in Sweden are small local drug trafficking crews, but a few others are bigger in scope or are satellite teams for bigger transnational organized crime groups. The most noteworthy seem to be;

Södertalje-network;
This group isn't directed from outside Sweden and it's very much a local conglomerate of several crime families that have an Assyrian background from Northern Iraq and Southeastern Turkey. It's also called the "Syriac Mafia" in Sweden and with more than 100 members it's one of the biggest organized crime networks in the country. Regarded to still be a very strong one because they're very much entrenched in the legal economy of their community and have a diversified portfolio of criminal activities.

Botkyrka-network;
This is actually the local Serbian/Montenegrin mafia and they're a local offshoot of a bigger organized crime group based in the Balkans (used to be directed from Belgrade, but I can't find any current information about this). As is the case with the Södertalje group, this also is one of the longest standing groups in the Stockholm region and with more than 100 members also one of the most powerful. Involved in multiple criminal activities and a few of the smaller drug trafficking groups are supplied by them and fall under their influence, the most well-known being the Varby-network.

Turebergs-network;
Used to be called the "Turkligan" because basically all of its members are Kurds from Southeast Anatolia. Allegedly an offshoot of the Diyarbakir-based heroin mafia and the heroin trade is their main business. With around 60 members this is still a noticeable presence in the underworld of Stockholm.

Hagsätra-network;
Allegedly they're connected to the Stockholm chapter of the Hells Angels. They're also called the "restaurant mafia" because through loansharking and protection racketeering they've managed to take over bars and restaurants. Aside from that they're also involved in drug imports and have managed to infiltrate the upper society as well through corruption. This network is more of a classic blue collar operation and his close to 50 members. Coupled with the 20+ members of the Hells Angels in the Stockholm area - who also have influence over one or two other local crime networks - it's clear that the HA's are still a substantial force in the Swedish underworld. They've only gotten smarter and more sophisticated and focus on financial crimes as well.

Dalen-network;
This seems to be a cooperation between a few noted gangland figures. The most famous are a former hockey player with Greek roots who has criminal connections in Greece and at the moment is hiding either in Spain or Greece and two brothers who are Bulgarian citizens and who are allegedly connected to a major Bulgarian organized crime group.

Foxtrot-network;
This group has influence over two smaller gangs named "Zero" and "Bro". The leader is an Kurd who immigrated from Iraq and who also has Turkish citizenship. Allegedly this network is connected to organized crime based in Southeast Anatolia as well and the leader right now said to be hiding in that region.
Are in a very violent conflict with the Greek from the Dalen-network.

Rinkeby-network;
Unlike most of the others this group is not connected to a bigger transnational criminal organization, but instead it's a local drug trafficking network consisting of mostly Somali gangsters. Used to be one of the biggest trafficking networks in the city and had major narcotics connections, but nowadays it has split into different warring factions. The two most infamous gangs that sprung from this network are Shottaz (which has by now also fallen apart into different rival factions) and 3MST/Dödspatrullen. This conflict is one of the most violent going on in Sweden right now and has spilled over into Denmark.

Those were the most well known in the Stockholm region. In Mälmo you'll also find that most of the noted local networks are offshoots of transnational OC groups;

The M-Wing is influenced by a crime family from Novi Pazar, which in turn is allegedly connected to the Rozaje Clan - a transnational crime group based in the Sandžak region of Montenegro.

The K-Wing is the Mälmo-based Albanian mafia and is said to be connected to a major clan based in Kosovo.

The Fakhro clan is a Mhallami-Lebanese clan that's connected to the Al Zein clan based in Germany.

The bikers are still around in Mälmo as well, are very much connected to the Stockholm chapters and prefer to stay more under the radar as well.

The same goes for Gothenburg;

Hjällbo-network, which is mostly just called the Ali Khan clan. Ali Khan is the largest Mhallami-Lebanese clan in Sweden. Whereas the Fakhro clan is mostly a side branch of the Germany-based Al Zein clan, the Ali Khan clan is big and powerful enough to be considered a separate entity.

Backa-network, a group which is largely Moroccan led and which is connected to Moroccan organized crime based in the Netherlands. They're involved in a violent conflict with the Ali Khan clan.

Asir-network, which is mostly regarded as the Gothenburg-based offshoot of the Södertalje-network (the "Syriac Mafia") from Stockholm.

Not much is known anymore about the Naserligan, which used to be the Gothenburg-based Albanian mafia and was also connected to a major Kosovo-based clan. At this moment they're probably largely dismantled.