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I would love to know all the differences between infantry types. I've searched somewhat on the internet and found a few, but I still have questions.

In the Blitzkrieg campaign, you have access to 8 different types of infantry. This is all I have come up with so far.

Garrison - Bonuses to entrenchment while stationed in city hexes (worst stats imaginable)
Pioneer - Ignore entrenchment value of enemies when attacking
Stosstruppen - ?
Jaeger - Moves through rough terrain such as mountains and marshes with no penalty
Fallschirm - Can be dropped from Air Transports anywhere on the map
Bridging - Acts as a clear terrain hex for allied units when stationed on a river hex.
Regular - Nothing.
Cavalry - Can move additional squares.

Does Stosstruppen do anything special? Or is it just the stats you're paying for? Pioneer and Stosstruppen have equal stats, but Pioneer ignore entrenchment. So, where there is enough money, I have no need for Stosstruppen, right?

The other nations have combinations of these infantry types (just a different name for them) plus or minus some
other types depending on the country. It would be cool and awesome to know what they all did.
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I think Stosstruppen have "Shock Tactics" and I also think that means that if they attack, the suppresion holds for the rest of the round.

I could be wrong.