Does anyone recognize this cap device?

I am not sure it has a military connection, it is only a guess from the red, white and blue inlays. It appears to be old - very old. I can see no stamped writing on it anywhere. It is about 13mm. The symbol containing the inlays is a Celtic Triangle, the three suggests also the Trinity and thus perhaps a religious connection. I have researched every possibility I can think of and find nothing. I thought perhaps it was an Army of the Potomac II Corps item, but do not really think so as it is not really a trifoil. I apologize for posting here if it is inappropriate - I have tried for a while now to register at other militaria forums but every attempt at doing so only results in my inability to view the posts already on those forums, which I was able to do before I had the temerity to try to register my unworthy self. Any help or thoughts deeply appreciated.
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Being decended from a very long thick line of Irish Catholics I suspect that it is an Irish Catholic fraternal society pin of some sort. Two such groups for example are the Ancient Order of Hibernians and the Irish Catholic Benevolent Union. There were many others particularly in the 19th Century and early 20 Century when anti-Catholic, anti-Irish sentiments and prejudices were extreme. The Celtic symbol engraved on the button is that of the Holy Trinity - which deductively suggests Catholic and Irish in origin. That the button appears to be a lapel button hole button since it has a pin to orientate it so it is pointing right way up. The colours could be significant in that they might designate the branch of the society, or a rank or office held.

Thank you Paul. The Hibernians had occurred to me and I did do some searching along that line, but unearthed nothing. I'll do a little more and look into the ICBU, of which I was ignorant. Usually I am able to identify this sort of item eventually, but this one is proving to be obscure.