I'm not sure what exactly you mean by "secret societies", but there were certainly groups that operated under the "official" radar and tried to keep their acts secret for a variety of reasons.

I already posted this as a response to another question, but that question got little attention, and it seems to fit pretty well here in any case: The secret Bacchanalian cult and the associated crisis of 186 BC.

Bacchus is the latinized form of one of the names for the Greek god Dionysos. In the Roman world, Bacchus became associated with the earlier Italian god Liber Pater, also a god of wine, drunkenness and fertility (essentially the kind of God Tyrion Lannister would like to see in Westeros). So essentially, a well established cult for a popular deity. But something changed in how this cult was practiced. Like all the things corrupting the virtuous Romans, this particular evil came out of the East, possibly from Anatolia, "like a pestilential disease", Livy tells us, introduced by a Greek - and, as he points out, not one of the great philosophers or scholars, but a simple priest and diviner. And one that conducted his business not out in the open, but performing his services in secret and at night. Who seemed to gather a large following rather quickly.

What made this priest out of the east and his interpretation of the Bacchus-cult so appealing? According to Livy, one of the things used to lure new followers into his services was providing wine and a meal, which is of course always popular. After that, the whole thing proceeded into a giant orgy, in which men and women did 'whatever their mind lusted after', not stopping at their own sex or even at small boys. Not content with that, they also forged documents, seals and testaments, and indulged themselves in rape and murder during their secret meetings, sounding drums and cymbals to mask the sounds.

This evil spread from Etruria to Rome and was finally brought to the attention of the consuls by one young Publius Aebutius. Publius, whose late father had been an equestrian, was living with his mother and step-father. They saw him as an obstacle to inheritance, and decided to remove him, by having him take part in the bacchanals as a victim (his mother had supposedly vowed to let him receive the bacchanalian rite in return for his reconvalescence from illness). However, his girlfriend, a whore but "noble of spirit" warned him of the danger that this posed to him. She had taken part in these rites while still a slave (she was a freedwoman by now) with her mistress, and so she knew what happened there - the priest would sound drums and trumpets and lead him to a dark place, where noone could hear him scream, and where he would have to be of service to the men of the cult, who, according to her preferred boys to women. If he didn't consent to his violation, they would have him killed. After she made him promise not to go, he got promptly kicked out of the house by his parents for refusing to let himself be introduced to the bacchanalian cult.

His aunt told him to bring the matter to the attention of the consuls, who launched investigations. They questioned Publius' girlfriend, Hispala, who reluctantly told them about how the cult had evolved into something that would as well fit into de Sades Justine as just another episode of orgies, homosexual libertinage and general frenzy and bloodlust. The consuls brought the matter before the Senate, and the Senators, shocked by the extent and the actions of this underground cult, saw the Republic endangered and ordered the consuls to destroy the cult, not only in Rome but in the whole of Italy, and furthermore prohibited all cultic meetings of the Bacchanalians in all of Italy.

Livy gives us a rousing speech of the Consuls on the forum to the general populace, informing them about the extent and the crimes of the cult, asking them how men should in the future protect them by the sword who had been sullied by passive sodomy (the bad kind of sodomy for a Roman male). He then reports the general panic in Rome, how many tried to flee the city but were apprehended at the gates, and how others were driven to suicide who were involved in the cult. The curule aedils were to apprehend the cult leaders, while the plebeian aediles should prevent the conduction of cultic meetings. A bounty was offered for people involved in these cultic meetings. An edict by the senate was proclaimed that pretty much placed all Bacchanalian worship under punishment unless specifically allowed by the urban praetor. Apparently, the investigations were quite successful. The ringleaders were apprehended, and accused together with 7.000 others. Those who were not involved in murder or rape were imprisoned, the rest, which were the majority, were executed. Bacchanalian shrines were destroyed through all of Italy.

What made the Senators and the elite so fearful of this cult that it provoked such a harsh crackdown, often called the first example of religious persecution by the state? Livy paints a nice picture, of the grave and ordered senate, concerned for the welfare of the Republic, contrasted with the 'unlicensed', un-public cult, following the dionysian values of seeking personal fulfillment and self-indulgence before duty to the state. The morale is quite clear: Organized religion, in the form of the public cults performed by the elite ensured the wellbeing and success of Rome as a collective. Selfishness and seeking personal satisfaction leads to sexual and moral corruption, and, ultimately destruction. One cannot help but notice that all of the ringleaders are plebeians, Marcus and Caius Atinius; while Lucius Opiternius and Minius Cerrinius were non-roman Italians. Also interesting is that the Greek who supposedly started this whole affair remains unnamed, which to me makes him likely nothing more than a literary device, part of the larger trope of the decadent hellenic influence on Rome so often bemoaned.

The problem is, there are only two sources on it. There's Livy (as well as later authors copying him, but adding nothing new), and the senatus consultum de bacchanalibus, a copy of the Senates edict, presumably once posted all over Italy, from the ager Teuranus, near modern Tiriolo. But this senatusconsultum might point to another reason: This edict showed the Italians just how powerful Rome had become. They were able to control the religious life of all the Italians. And controlling religious life back then also meant influence on politics. It is often cited as one of the drops of increasingly overbearing Roman control over the life of the non-Romans of Italy which finally resulted in the Social war of 91-88 BC.

P.S.:The whole affair had a very happy ending for Publius and his Hispala: each was awarded 100.000 As, Publius was freed of military service (one of the higher honours of the state for a citizen), and Hispala was made equal to a freeborn woman in status.