I dug one of mine up last autumn, and used a large (9 inch) serrated garden knife to divide it. Yes, it's brutal, but most of the time it works. I now have nine new plants. I could have had more, but ended up ditching about one third of the original.
Okay, I've not yet cleaned it from today's usage - but I will!!
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I live in west central Scotland - not where that photo is...