Inspired by the nice post and this, apart from SU(N), now I am particularly looking into the exact sequences of SO(N), but I will like to loosen the conditions of the previous post,
Q1. $$1 \to A \to SO(N) \to B \to 1$$
where any of $A$,$B$ can contain finite group or discrete groups.
I am further interested in just three cases SO(8), SO(9), SO(10),
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Q2. $$1 \to A \to SO(n) \to B \to 1$$ I wonder whether, when there is any example such that $A$ $$A=U(1) \times SU(2) \times SU(3)\;\;\; \text{or} \;\;\;A \supseteq U(1) \times SU(2) \times SU(3)?$$ (there can be an additional discrete finite group parts for $A$ such as additional $\mathbb{Z_N}$) or whether there is any example such that $B$ $$B=U(1) \times SU(2) \times SU(3)\;\;\; \text{or} \;\;\;B \supseteq U(1) \times SU(2) \times SU(3)?$$ (there can be an additional discrete finite group parts for $B$ such as additional $\mathbb{Z_N}$)