Snatchers are a group of wizards and humanoid creatures that support Voldemort. The organisation was founded by Voldemort himself shortly after seizing control of the Ministry of Magic. Snatchers prowl the country and capture any Muggle-borns, [Mudblood] or blood-traitors. Snatchers are also alerted to anyone using Lord Voldemort's name which has a Taboo curse placed upon it by Voldemort himself. This organisation is a lot less regimented than the Death Eaters, an organisation of witches and wizards closer to Lord Voldemort.
 Summary of the Snatchers
The Snatchers are a legion of witches and wizards who have a lower ability when it comes to performing magic. In the Harry Potter series the Snatchers are portrayed as quite unintelligent and their lack of combat skill is evident in chapter twenty-three of Harry Potter and the Deathly Hallows. Upon arriving at Malfoy Manor with Harry, Ron and Hermione as their prisoners, four Snatchers including both Fenrir Greyback and Scabior lose to Bellatrix Lestrange in a duel.
"Stupefy", she screamed, "stupefy!" They were no match for her, even though there were four of them against one of her: she was a witch, as Harry knew, with prodigious skill and no conscience. They fell where they stood, all except Greyback, who had been forced into a kneeling position, his arms outstretched. - Harry Potter and the Deathly Hallows, Chapter Twenty-Three pg. 374
"They weren't the brightest. One of them was definitely part troll, from the smell off him..." - Harry Potter and the Deathly Hallows, Chapter Twenty-Three, pg.311
It is thought that Snatchers who had proven their skill were recruited to the Death Eaters by Lord Voldemort.
Unlike the Death Eaters, Snatchers have no set uniform. Instead they wear casual clothes such as hoodies, sweatshirts and jackets, making each Snatcher rather unique. Arguably their chosen outfits are quite intimidating especially when seen as a large mob. Additionally all Snatchers have a red tie around one arm to signify their allegiance to the organisation and Lord Voldemort. This is yet another parallel to the Nazi Gestapo (see section below).
In the book we first hear of the Snatchers via Ron Weasley. After Ron returns from his hiatus from the Horcrux hunt, he explains how he was cornered by five Snatchers.
"Snatchers", said Ron. "They're everywhere, gangs trying to earn gold by rounding up Muggle-borns and blood traitors, there's a reward from the Ministry for everyone captured. I was on my own and I look like I might be school age, they got really excited, thought I was a Muggle-born in hiding. I had to talk fast to get out of being dragged to the Ministry." - Harry Potter and the Deathly Hallows, Chapter Nineteen, pg.311
Ron is able to steal two of their wands and apparate to a place in which Harry and Hermione had been camping previously. In the movie adaptation we see the Snatchers at an earlier point in the story, in Harry Potter and the Deathly Hallows Part One. Harry orders Kreacher to track down Mundungus Fletcher after he stole Salazar Slytherin's locket. In this scene we see a group of Snatchers pushing and shoving their way through Diagon Alley forcing Mundungus to duck into an alleyway.
Later in the book we hear of the Snatchers murdering Ted Tonks, Dirk Cresswell and Gornuk, all whom are part of a group with Dean Thomas and other allies of Harry. These murders are revealed in Chapter Twenty-Two, The Deathly Hallows via a secret radio transmission called Potterwatch.
This is the same group that finds Harry, Ron and Hermione later in the chapter. Harry accidentally activates the 'Taboo curse' by saying Voldemort's name and this gang of Snatchers, led by Greyback in the book, apparate outside the trio's tent. Upon investigation Harry, Ron and Hermione try to pose as other people; Vernon Dudley, Barny Weasley and Penelope Clearwater. Despite Hermione casting a Stinging Jinx to transform Harry's face, his scar is still recognisable to the group of Snatchers. Hermione's true identity is also revealed after the Snatchers see her face in an issue of the Daily Prophet.
The trio are then taken to Malfoy Manor after being caught in which Draco Malfoy is asked to identify them.
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