Non split extension of lie algebra?

Is there a Lie Algebra $\mathfrak g$ so that the extension

$0\xrightarrow{}\mathfrak h\xrightarrow{}\mathfrak g\xrightarrow{}\mathfrak q\xrightarrow{}0$

does not split, i.e. $\mathfrak g$ is not a semi-direct product of $\mathfrak h$ and $\mathfrak q$?
As I understand it, $\mathfrak q$ should not be identifiable with a subalgebra of $\mathfrak g$, right? Since $\mathfrak h$ is already an ideal in $\mathfrak g$ as the kernel.

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