Why is the height of a satellite greater than the apogee of its orbit? I read in the German Wikipedia for the Indian Technology Experiment Satellite, that the apogee (Apogäumshöhe) is 567 km, while the height of the orbit (Bahnhöhe) is 572 km. I had always thought that the apogee is the furthest point of the orbit from the Earth and I wonder how can there be a height greater than that.
You are right!

Apogee is higher than Perigee, except when the orbit is perfectly circular when they're equal.
Semi-major axis will be half-way between the two.
572 km doesn't make sense.

As pointed out in comments, expressed like this they are the distances from Earth's center minus a fixed equatorial radius of the earth, in this case about 6378.137 kilometers. From the numbers in Wikipedia for peri and apo you'd call this a 567 x 515 km orbit. It's a simple way to express roughly the size and shape.
The linked de.Wikipedia page says
Umlaufzeit:       95,3 min[1]
Bahnhöhe:         572 km
Bahnneigung:      97.7°
Apogäumshöhe:     567 km
Perigäumshöhe:    515 km

[1]  Bahndaten nach [TES](https://www.n2yo.com/satellite/?s=26957). N2YO, 18. November 2017, abgerufen am 18. November 2017

I don't know what Bahnhöhe means, google translates it as &quot;track height&quot;, so I've asked What exactly would a distance labeled Bahnhöhe mean in the context of a satellite's orbit around the Earth? in German SE.
While the data might be static, the mentioned n2yo link says:
NORAD ID:           26957 
Int'l Code:         2001-049A 
Perigee:            513.2 km 
Apogee:             564.0 km 
Inclination:        97.7 ° 
Period:             95.3 minutes 
Semi major axis:    6909 km 

and looking it up in Celestrak gives the two line element set or TLE as
TES                     
1 26957U 01049A   20269.88561907  .00000195  00000-0  15464-4 0  9995
2 26957  97.7413  31.7408 0036778 246.8588 112.8763 15.11565287 39121

The TLE is also shown in n2y0.
Here's a link direct to Celestrak for this object. They are always changing, the orbits of Earth satellites are never really fixed.
Atmospheric drag tends to lower them and Earth's lumpy gravity causes them to precess, just for starters.
Many satellites have small thrusters to raise their orbit after atmospheric drag lowers it, so we can't expect numbers in static Wikipedia data fields to be accurate.