HERMAN and the Hermits - his backing group for the past six years - may split to follow separate careers before the end of the year.     Herman, real name Peter Noone (22), a former "Coronation Street" child actor, has received several solo offers. Among them is a film test, a starring role in the American presentation of the London smash stage show "Charlie Girl," and a chance of his own TV series.     And the Hermits - Karl Green, Derek Leckenby, Barry Whitwam and Keith Hopwood - are known to be considering working on their own. Recently, during the group's London panto season with Herman, the four have been working on their own stage act.     Group's manager Harvey Lisberg said this week: "The Hermits are at present simply insuring their own future. They've improved four million per cent - and could now go on the road without Peter. I don't think they want to work together anymore when the recording contract runs out in December. None of them want to do one-nighters for the rest of his life."     Herman's Hermits hit stardom in 1964 with I"m Into Something Good," followed by successes like "No Milk Today," "My Sentimental Friend" and "There's A Kind of Hush." In America, they once rivalled the Beatles' popularity and had million-sellers with songs like "Mrs. Brown, You've Got A

Lovely Daughter." They've sold around 50 million records.     Recently, however, the Hermits were reported to be unhappy - mainly because the group hasn't been working. Their last release, "Here Comes The Star" failed to make the chart ... and rumours of unrest have been rife.     Herman's Hermits' recording contract with producer Mickie Most expires in December.     Says manager Lisberg: "Peter won't stop working on his own; and he'd like to keep the Hermits going too. The reason for the rumoured discontent was the fiasco over the last record. These feelings haven't developed overnight. The same thing happens about every six months."     He added: "We've been trying to get Peter his own TV series and we were approached for him to star in "Charlie Girl" in the States.     "I honestly don't know what will happen in December. I'd be very happy if they could both get hits on their own. I believe Mickie Most could find the Hermits a hit with his eyes closed."     Mickie Most, who set Herman's Hermits on the road to chart fame, told Disc: "I personally can't ever see a split. They fit together so well, it would be silly for them to fall apart because of their egos."