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how many injective homomorphism between two lie algebra sl2 and sp6 up to conjugate by Sp6?

how many injective homomorphism between two lie algebra $sl_2 $and $sp_6$?sp_6$ up to conjugate by$Sp_6$ ?

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how many injective homomorphism between two lie algebra sl2 and sp6?

how many injective homomorphism between two lie algebra $sl_2 $and $sp_6$?