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108 = 2² * 3³
Thus there are six nonisomorphic abelian groups of order 108,
(1) Z₃ ⊕ Z₆ ⊕ Z₆
(2) Z₃ ⊕ Z₃ ⊕ Z₁₂
(3) Z₆ ⊕ Z₁₈
(4) Z₃ ⊕ Z₃₆
(5) Z₂ ⊕ Z₅₄
(6) Z₁₀₈