Left altar radical (side-form of 示) - picturing a stone altar where offerings were laid. Anchors 神 in the meaning of spirit, divinity, the unseen powers worshipped at the altar. Same spirit family: 福 (blessing), 祖 (ancestor), 礼 (ritual), 祝 (pray).
Right 申 supplies the sound (shēn to shén, just a tone shift) and adds rich semantic flavor: 申 originally pictured a lightning bolt zigzagging from the heavens - the most ancient sign of divine power. Pairing the altar with lightning gives the perfect picture of a deity. Same phonetic family: 伸 (extend), 绅 (gentry), 呻 (groan).