There are two versions of the Pentium II: the original Klamath at 350 nm, and the shrunken Deschutes at 250 nm.
Deschutes generally overclocks well, especially the later ones. Intel could have sold 500 MHz ones (5x100), but decided to artificially limit them to 333 MHz (5x66), presumably to keep them from competing with the new Pentium III.

Scali wrote:

There are two versions of the Pentium II: the original Klamath at 350 nm, and the shrunken Deschutes at 250 nm.
Deschutes generally overclocks well, especially the later ones. Intel could have sold 500 MHz ones (5x100), but decided to artificially limit them to 333 MHz (5x66), presumably to keep them from competing with the new Pentium III.

Interesting. Mine has the Deschutes core.

SL2TV was an overclocking favorite at the time. Regardless, 560MHz is impressive! The deschutes core has plenty headroom by itself, but the L2 cache rating is the deciding factor for these processors. Cartridges could ship with cache rated just sufficient, or with faster cache, depending on the supplies at the fab at a certain time. Your specimen is equipped with cache that was intended for faster models.
The downside of these late productions: they are multiplier locked. In addition the P3 Katmai 550 or 600MHz is just as easy to get these days, which is kinda the same thing, just with some SSE on top.

tpowell.ca wrote:

Is the Pentium II typically that friendly to overclocking?

No, not that friendly.
Mine never went above 417MHz whatever the voltage, with active L2. On the other hand, I've seen klamaths at 450 with active cache, so... , luck of the draw as usual.
L2 cache will usually be the limit, and you must have a cpu with higher than standard L2 cache speed for a 333MHz processor.
Core itself reached 450MHz commercially before being replaced by katmai.
Celeron was much better at this game.

tpowell.ca wrote:

I was testing different system configurations on my Gigaby GA-6BXC motherboard comparing CPUs when I accidentally ran my Pentium […]
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I was testing different system configurations on my Gigaby GA-6BXC motherboard comparing CPUs when I accidentally ran my Pentium II 333 MHz (SL2TV) at 560MHz (112MHz x5.0)!
The CPU was not overvolted and ran all benchmarks in DOS and Windows 98 for hours without a single glitch.
Quake, DOOM, 3DMark99, 3DMark2000, Sandra, Quake 2 and Quake 3.

That's a 68% overclock, and the CPU never even got hot. I didn't notice the massive overclock until I started to compare the results to a 500MHz PIII Katmai which it inexplicably (but now understandably) destroyed.

Is the Pentium II typically that friendly to overclocking?

Congratulations are in order !
500MHz or so was quite common, you got 504MHz with that 4.5 multipel CPU and 112MHz FSB.
But 560 was not common.
And for that reason the P2-333MHz chips were less favored compared to the 300's (SL2W8/SL2YK !).
A 300MHz SL2W8 was pretty much guaranteed to do 450MHz with minimal effort and stock cooler.
But with a 333MHz the odds of reaching were something like 50-75% (guessing here from my own experiences).