Okay I see, that sounds really bad.
I now found out, that the model gets that bad, because I removed one univariate outlier.
Before the indices were still far from perfect but not that bad at all: chi²/df = 1,988, CFI = 0.818 TLI = 0.776 RMSEA = 0.144 and SRMR = 0.089.
Is that possible? To me...