Answer: Very early spring would be a better time to try to take a division from the shrub. The reason for this is that summer is hot and stressful on a plant trying to form new roots. To take the division you would need to dig down carefully and take a nice piece of root attached to a top portion, perhaps the diameter of a pencil. Plant it in good rich soil and a sunny location and keep the soil moist (not sopping wet) until the plant becomes established.
Another method would be to take a tip cutting in June. Take a tip about four to six inches long, remove leaves from the bottom portion and dip the cut end in rooting hormone. Plant in damp soilless mix and cover with a plastic bag to maintain humidity. Set it in a bright location out of direct sun and roots should form in about two months. Open the bag occasionally to allow for air exchange and to release any excess humdity if condensation forms.
The newly rooted plant can be set out in the early fall and mulched well for winter.
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