The notions of symmetry group and camouflage are explained, and a technique is introduced to visually camouflage symmetry groups in natural textures. Two experiments were carried out to test discriminability of symmetry groups p1, p2, pm, and pg in 4-oddity and 5AFC designs with different or same texture per set of stimulus pictures, respectively. In 4-oddity, detection of p1 was enhanced by pm distractors and impaired by those of pg. In 5AFC, p2 proved discriminable against p1; pg did not. Findings are interpreted as qualifying broad claims about symmetry as an organisational principle for vision. Further investigations of visual discrimination of symmetry operations and groups are suggested.