Subgroup notation on Wikipedia

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Surfing wikipedia about finite groups, I see a lot of notation similar to that found in this section (image below). Its meaning is not clear to me and I didn't find an explanation on wikipedia. Could anyone elaborate?

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As mentioned in the comment by Derek Holt, this is the notation used in the book "ATLAS of Finite Groups".

In particular, $2^{1+24}.Co_1$ means a group with a normal subgroup $N$ that is an extraspecial group of order $2^{25}$ and such that the quotient group $G/N$ is isomorphic to the first Conway simple group, $Co_1$.