
errichten
to erect
To build or put up something large or important, especially buildings, monuments, or other structures.
Die Stadt plant, eine neue Brücke über den Fluss zu errichten.
The city plans to erect a new bridge over the river.
to erect / establish
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to erect
To build or put up something large or important, especially buildings, monuments, or other structures.
Die Stadt plant, eine neue Brücke über den Fluss zu errichten.
The city plans to erect a new bridge over the river.

to establish
To found or build up something abstract such as an organization, a system, or a rule.
Nach dem Krieg wurde eine neue demokratische Regierung errichtet.
After the war, a new democratic government was established.
'Errichten' (to erect / establish) is an inseparable verb. The prefix 'er-' remains firmly attached to the verb stem 'richten' in all tenses and sentence constructions.
Man errichtete das Monument im Zentrum der Stadt.
The monument was erected in the center of the city.
The word 'errichten' (to erect / establish) is formal and is used for large, important, or official construction projects and foundations. You would not use it for building a garden shed.
Die Firma wird auf dem Gelände einen neuen Hauptsitz errichten.
The company will erect a new headquarters on the site.
You can tell whether the concrete or abstract meaning is intended from the object. If it is a structure (building, monument), it is the concrete meaning. If it is a system (state, rule), it is the abstract meaning.
Ein Denkmal für die Opfer des Krieges wurde errichtet.
A monument to the victims of the war was erected.
In the meaning 'bauen' (to build), 'errichten' (to erect) is typically combined with large structures: 'ein Gebäude errichten' (to erect a building), 'ein Denkmal errichten' (to erect a monument), 'eine Mauer errichten' (to erect a wall), or 'eine Sperre errichten' (to put up a barrier).
An der Grenze wurde ein hoher Zaun errichtet.
A high fence was erected at the border.
to found / be based on
Gründen is the usual term for bringing a new organization into being. Errichten can also refer to creating an abstract organization or system, but sounds more formal or institutional. For an ordinary association, gründen is therefore usually the better choice.

Der Verein errichtet ein dauerhaftes Hilfssystem für bedürftige Schüler.
The association is establishing a permanent support system for students in need.
Die Eltern gründen einen Verein zur Unterstützung der Schule.
The parents are founding an association to support the school.