Groetzsch Graph planarity [closed]

(1) Prove that the Groetzsch Graph is not planar.

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closed as off-topic by Dan Rust, T. Bongers, Serkan, Eric Naslund, Bruno JoyalNov 25 '13 at 3:36

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4-colour-theory is difficult, 2-coour theory is easy. – Hagen von Eitzen Nov 20 '13 at 7:24
ad (2): One cannot colour the faces of a cube with two colours only!! – Hagen von Eitzen Nov 20 '13 at 7:25

For (1) recall that a graph is non-planar if and only if it contains a subgraph that is a subdivision of either $K_5$ or $K_{3,3}$. So can you find such a subgraph? (Hint: $K_5$ works for this case).