What are some explicit examples (e.g., by explicitly describing its Hopf algebra) of finite unramified group schemes? (Ie, the sort of group schemes which appear as automorphism groups of objects parametrized by Deligne-mumford stacks).

For example, I'd be interested in finite unramified group schemes over $\mathbb{C}[[t]]$ which are not flat - e.g., they are generically etale, but the cardinality of its special fiber may jump.

Is there a good reference for such objects? Are there structure theorems for such things? (For example, does every finite unramified group scheme over $\mathbb{C}[[t]]$ admit a "maximal finite etale quotient"?)