Here is what Poincare wrote, in a widely distributed June 5, 1905 paper:
The essential point, established by Lorentz, is that the electromagnetic field equations are not altered by a certain transformation (which I shall call after the name of Lorentz), which has the following form: ...
The sum of all these transformations, together with the set of all rotations of space, must form a group; but for this to occur, we need l = 1 so one is forced to suppose l = 1 and this is a consequence that Lorentz has obtained by another way.
Einstein's famous paper was received by the journal on June 30, 1905. It gives the velocity addition formula, and adds:
from which we see that such parallel transformations — necessarily — form a group.This only applies to parallel transformations, or what we would now call Lorentz boosts in the same direction. That is, it is a one-parameter group. There is no other mention or use of the group concept.
It appears to me that Einstein read Poincare's paper, and added the sentence about the group, without even much understanding of what a group is.
Lorentz credited Einstein for this observation in 1906, as it is not clear that Lorentz realized that the inverse of a Lorentz transformation is another Lorentz transformation.
What Poincare calls the "Lorentz group" is a 6-dimensional group, not a one-dimensional group.
Einstein always claimed that he had not seen Lorentz's 1904 paper, but no one believes him. He was even cagey about whether he had read Lorentz's 1895 paper.
The commenter goes on to credit Lorentz and Einstein for showing the covariance of Maxwell's equations.
Lorentz showed in 1895 that Maxwell's equations corresponded to similar equations in another frame, via what we call now Lorentz transformations. He improved this to higher velocities in 1904, in response to Poincare badgering him about the relativity principle. Einstein showed essentially the same thing in 1905, as I explain here.
It is not possible to understand covariance unless you first understand what the group is. Covariance means using the group to transform the equations, including the fields and everything else.
We know that Einstein did not understand covariance until about 1915, because he had to be tutored on the subject by Grossmann and Levi-Civita, and some of his publications showed misconceptions.
Poincare showed covariance of Maxwell's equations in the Palermo paper (Received July 23, 1905; Printed December 14-16, 1905; Published January 1906). Minkowski was much more explicit about it in his 1907 paper that cites Poincare's Palermo paper.
The Lorentz group and the covariance of Maxwell's equations are right at the core of what we call special special relativity, and these concepts are almost entirely due to Lorentz, Poincare, and Minkowski. Some early contributions were made by FitzGerald, Larmor, and others. Einstein contributed nothing to these concepts, and it is doubtful that he even understood them until many years later.