διδάσκειν δὲ γυναικὶ οὐκ ἐπιτρέπω, οὐδὲ αὐθεντεῖν ἀνδρός, ἀλλ' εἶναι ἐν ἡσυχίᾳ.
I looked this up in some of the older commentaries - Ellicott, Fairbairn, Bernard, Kelly - they all take it for granted that διδασκειν here is intransitive. For example, Kelly:
But to teach I permit not a woman nor to exercise authority over a man, but to be in quietness
with a footnote:
The emphatic place is restored in accordance with א A D F G P, many cursives, Vulg. Goth. Arm. etc, and so I imitate in English.
More recently, Fung writes (in The Church in the Bible and the World, pp 198-9):
Some scholars take andros as the object of both didaskein and authentein, the sense being that in the life of the church of woman is not permitted to 'teach or have authority over' a man; and since teaching and having authority (equated with ruling) are among the chief functions of the presbyteros or episkopos (cf. I Tim. 3:2; 5:17) - the presbyter-bishop gives the congregation authoritative teaching which is enforced by means of church discipline — Paul is taken to mean that women are prohibited from serving in ruling and teaching offices or functions. To this way of construing the grammatical function of andros, it has rightly been objected that it is 'too far removed from "to teach" to be understood as qualifying the meaning of that verb as well'; if Paul's intention had indeed been to say 'I do not permit a woman to teach men or to have authority over a man' he would probably have written either didaskein andra . . . ouk epitrepo oude authentein andros or, if that be considered a little clumsy, didaskein andra . . . ouk epitrepo oude authentein [sc. andros], to judge by similar constructions with ouk . . . oude.
The relevant footnotes:
191 E.g. Knight, Role Relationship 30, 49, 51, 52; idem, 'Role Relationship' 84-85; Foh, Women 125-126, 239, 248.
192 Payne, 'Libertarian Women', 175.
193 With the first suggestion cf. 1 Jn. 3:6b, pas ho hamartanon ouch hed raken auton oude egndken auton', with the second suggestion cf. Jn. 14:173, hoti ou thedrei auto oude ginoskei (sc. auto). From the Pauline writings, two of the passages referred to in the next note seem to offer help here: Rom. 8:7 to . . . nomo tou theou ouch hypotassetai, oude gar dynatai Gal. 4:14 kai tonpeirasmon hymon . . . ouk exouthene sate oude exeptysate. While neither of these examples exactly repro duces the structure of i Tim. 2:12, in both of them the ou clause is complete in itself and the complement or object of the verb after oude is to be supplied from the ou-clause. With Gal. 4:14 cf. Heb. 10:8, thysias . . . ouk ethelesas oude eudokesas.