Step 1: Understanding the Question:
This question tests knowledge of insect orders and their common names.
Step 2: Detailed Explanation:
The order Dictyoptera includes cockroaches and mantids.
Grasshoppers (A): Order Orthoptera.
Leafhoppers (B): Order Hemiptera.
Moths (D): Order Lepidoptera.
Thus, cockroaches belong to Dictyoptera.
Step 3: Final Answer:
Thus, the common name of insects of the order Dictyoptera is cockroaches, which corresponds to option (C).
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