Yes - You can cast metamagic-enhanced spells into a spell glyph (except for empowered)
You can store a prepared spell of 3rd level or lower in the glyph by
casting it as part of creating the glyph. (PHB)
All the metamagic abilities except empowered say:
When you cast a spell... (PHB)
So, because you are still casting the spell (per the description of spell glyph) and you can apply metamagic whenever you cast a spell per the metamagic description, I see no reason why this would not be allowed.
It is worth noting also that ring of spell storing which works in much the same way as spell glyph, specifically restricts the qualities that the spell stored in the ring can keep. Since there are no such restrictions here, the most straightforward interpretation is that the spells are stored exactly as the caster casted them (including metamagic).
Empowered spell is a special case that only works with the spell after the glyph has triggered
Empowered spell is the only metamagic ability that can (and RAW must) be applied after the casting of the spell has taken place. Thus, it must be addressed separately.
Thus, you shouldn't even need to apply this metamagic ability when you cast it, but can wait until it is triggered.
Can you cast an empowered spell into a spell glyph? - No
Empowered spell says:
When you roll damage for a spell...
RAW imply no, because you only apply empowered spell when you are rolling damage for the spell which means this takes place after a spell has taken effect.
And spell glyph says specifically that the spell's effects are delayed:
The spell being stored has no immediate effect when cast in this way.
The reason that empowered is written like this is because it allows the sorcerer the chance to spend the points to use the ability only if damage is actually going to be applied. Thus, for example, an enemy making their save and taking no damage from your spell would not result in you wasting sorcery points.
So, RAW, you cannot cast an empowered spell and store it in a spell glyph.
Can you apply empowered spell to a spell after spell glyph
triggers? - Yes
This answer depends on if the triggered spell is considered by your group to be cast by the sorcerer or if the glyph is considered to be a proxy for the caster. This is a matter that is not precisely clear RAW, and is talked about in this Q&A.
In the end, it makes sense to allow the sorcerer to apply the metamagic to the spell since they are the ones who cast it originally and the glyph is only acting as a proxy to cast it for them.
Allowing does enable some weird situations. For example, the remote nature of the spell would mean that you could be miles away or even on a different plane (thanks @Marq) from the glyph when it triggers. Allowing the spellcaster to modify the spell with empowered would mean that they could then modify the spell from basically anywhere, which many not make a whole lot of mechanical or thematic sense. But not everything in D&D5e fits perfectly together. Use common sense if you are DMing the situation and if you are the player don't expect the DM to allow you to do anything.
So, in the end, the easiest way to handle this situation would be to say that the spellcaster can apply empowered to the triggered spell.