This question has, and continues to, bedevil me in the ongoing NQM Barbarossa campaign. As German Divisions bled manpower from their original orbats of 17,200 troops with 3 regiments of 3 battalions each, they would have begun to resemble the 1944 orbat which was formalised at 12,400 men with 2 regiments of 3 battalions, or more commonly 3 regiments of 2 battalions each[1,2]
Gratuitous shot of an army group level (Heeresgruppe) ‘Karl-Geraet‘ self-propelled siege mortar. It gets an occasional outing when it catches up with the front line at a major city and has been seen no more frequently at the front than its historical counterpart.
Of these 12,400 men, 6,800 or 55% were combat troops  although Kershaw gives as high as 84.5% . Reducing the neu art ’43 or’44 orbat on the NQM 30:1 scale, a division contained the following  :
(1) Anti-tank gun (37mm/50mm/75mm/76.2mm) (S3) + limber (S3)
(0-1) 120 mm Mortar (at RHQ in 1st infantry regiment) (S3)*
(1-2) 81mm Mortar (at RHQ in 1st-3rd infantry regiment) (S3)*
(0-1) Infantry howitzer (75mm/150mm 3rd infantry regiment) (S3)*
(1) 105mm howitzer (in artillery regiment) (S3) + limber (S3)
(1) Flamethrower (in pioneer battalion) (F3)
(1) 20mm anti-aircraft gun (in artillery regiment) (S3)*
*these may be shown with horse-drawn limbers or not as they were sometimes man-handled tactically.
The orbat at the start of Barbarossa was : RHQ (CF3), Support ( regimental gun) (S3), 3 battalions each of Command + MMG + Mortar (CS3), 3 rifles (F3) : a total of 20 bases equalling 8 stands.
The neu art orbat was : RHQ (CF3), Support (regimental gun/81mm/120mm mortar) (S3), 2 battalions each of Command + MMG (CS2), 3 Rifles (F3) : a total of 12 bases equalling 6 stands.
Each infantry battalion lost 1 rifle company per battalion, leaving it with 3 rifle companies and a machine gun company.
Mention is made in non-mobile infantry units of the reconnaissance (recce) battalion being replaced by a fusilier battalion of equal strength to an infantry battalion, with horses and cycles provided for mobility of at least one company. For simplicity, I would mount both stands on horses/cycles.
The engineer battalion lost its bridging train to (presumably) army level and concentrated on its role of laying mines and being assault pioneers.
Artillery became increasingly self-propelled (SP), although SP units were concentrated in panzer and panzer grenadier divisions . Non-mobile infantry continued to make do with horses as motive power .
However looking at, for example, the manpower strengths at Stalingrad, von Paulus had 19 Divisions with “nearly a third of a million men”. This figure is more than adequate to accommodate 12,400 per division, but army troops would have taken a fair slice out of this figure. It is fair to say that if 30% to 50% reductions took place as Barbarossa progressed then it is reasonable to assume that at times German divisions contained no more strength than 3-4 battalions in a division. Another way of putting it, is that regiments looked more like battalions with integral regimental support and a division looked more like a British brigade.
 Zetterling, N. and Frankson, A. (2000) Kursk 1943 – a statistical analysis. Frank Cass, Oxford
 Tactical and Technical Trends, No. 7, Sept. 10, 1942.
 Beevor, A. (1998) Stalingrad. Viking, Harmondsworth
 Kershaw, R.J. (1987) Lessons to be Derived from the Wehrmacht’s Experience in the East 1943-45. RUSI 132(3), London