FACTBOX: Who are Somalia's al Shabaab rebels?

(Reuters) - A suicide bomber killed at least 19 people including three Somali government ministers Thursday at a graduation ceremony in a Mogadishu hotel. The bombing showed once again the insurgents' ability to strike the government at will, and suspicion for the blast immediately fell on the al Shabaab group which controls large swathes of the country.

Here are some details about al Shabaab:

* WAGING WAR IN SOMALIA:

-- Al Shabaab, which means "Youth" in Arabic, is an al Qaeda-inspired militant group that has taken control of large areas of south and central Somalia. The Horn of Africa nation has been mired in anarchy since warlords toppled military dictator Mohamed Siad Barre in 1991.

-- The interim government's attempts to restore central rule have largely been paralyzed by infighting and the Islamist-led insurgency. Fighting has killed more than 19,000 people since the start of 2007 and uprooted at least 1.5 million civilians. The chaos has also helped fuel kidnappings and piracy offshore.

-- Al Shabaab's hardline militia was part of the Somalia Islamic Courts Council (SICC) movement that pushed U.S.-backed warlords out of Mogadishu in June 2006 and ruled for six months before Somali and Ethiopian forces ousted them.

* HARSH PRACTICES:

-- In June, al Shabaab officials in one of the group's Mogadishu strongholds ordered four teenagers to each have a hand and a leg cut off as punishments for robbery.

-- Al Shabaab's hardline interpretation of Islamic law has shocked many Somalis, who are traditionally more moderate Muslims. Some residents give the insurgents credit for restoring order to the regions under their control.

* FOREIGN FIGHTERS:

-- The Somali government says hundreds of foreign fighters have joined the insurgency from countries including Afghanistan, Pakistan, the Gulf region and Western nations such as the United States and Britain. Some of the foreign jihadists have taken up leadership positions in militant groups including al Shabaab.

-- One American national of Somali origin was killed while fighting for al Shabaab in Mogadishu in July.

-- Also in July Australian police arrested four men linked to the group, raising concern it may be seeking targets outside Somalia.

-- On September 17, al Shabaab insurgents struck the main African Union military base in Mogadishu with twin suicide car bombs and killed 17 peacekeepers. Rebels said the bombing was revenge for the U.S. killing of Kenyan-born Salah Ali Saleh Nabhan, a most wanted al Qaeda militant.

-- Al Shabaab has threatened to strike Uganda's capital Kampala and Burundi's capital Bujumbura because both nations contributed troops to the 5,200-strong AU peacekeeping force AMISOM.