Not necessarily enormously helpful, but the best I can manage. The following is from Chapter 2, Short Account of the Development of the Russian Land Forces in Captain J M Grierson's "The Armed Strength of Russia" (War Office, London, 1886),
Page 18 has a table showing the army at the beginning of the Crimean War, 6 Army Corps – 18 Divisions* (72 regiments), 6 Rifle battalions (*each 2 line and 2 rifle regiments).
Page 20 – "the army was … by the 1st January 1860 reduced to 624 battalions … The organisation in force up to the time of the Crimean Was was, however, retained."
"In the years 1862 and 1863 radical changes in the organisation of the Russian Army were made by the Emperor Alexander…"
"… in 1870, at the outbreak of the Franco-German War, the Russian Army consisted of: …". The table shows
40 Divisions of Line Infantry (160 Regiments) – 500 battalions
4 Guard, 4 Grenadier, 21 Line Rifle Battalions – 29 battalions.
Page 21
1870 – The 1st and 2nd reserve Rifle Battalions became active. The Rifles were organised in 1 Guard, 1 Caucasian and 5 Line Brigades, as at present, and the remaining 8 reserve Rifle Battalions became Line reserve battalions, giving 80 in all of the latter.
Page 22
1873-74 Brigades were formed in both Infantry and Cavalry Divisions. Hitherto the regiments had been directly under the Divisional Commander.
Page 23
1880 The armament of the Infantry with the Berdan rifle, begun in 1876, was completed.