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Answer by Derek Holt for What are all possible subdirect products of two...

The answer to your question "is $H \cong G_1 \times Z_2$ or $Z_1 \times G_2$" is no (i.e. not necessarily).As an example, the Schur Multiplier of $A_6$ is cyclic of order $6$, so we take $G_1$ and...

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What are all possible subdirect products of two quasisimple groups?

Let $H$ be a proper subdirect product of two quasisimple groups $G_1$ and $G_2$. We know from the definition of quasisimple group that all the normal subgroups of $G_i$ live in $Z(G_i)$, the center of...

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