I asked a similiar question some five or six years ago.

The response I got was that a battalion could be anything from two companies or more.

An example was given of the Irish Brigade of Chicago, I belive the 21st. Illinois. Perhaps the 23rd.

They went into the Battle of Kernshaw, 1864, with 225 +/- and lost half their men. Their Col. Mulligan, then commanding the divison was mortally wounded. They were subsequently retitled as a battalion.

In my Confederate 43rd Tennessee, many times they were split into a left & right wings, five companies each. Somethimes they were referred to as battalions during these splits.

George Martin
St. Thomas, USVI