The majority of the radishes I harvested were of this form - bent so that part grew parallel to the soil above the ground, with the stalk taking another 90 degree turn to return to vertical.
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This appears to be typical root-knot nematode damage. You may have had infected mustard-family plants growing in the area before, and not realized it.
These are difficult to control. I usually manage them with crop rotation. Here's a useful bit from UC IPM:
Management of nematodes is difficult. The most reliable practices are preventive, including sanitation and choice of plant varieties. You can reduce existing infestations through fallowing, crop rotation, and soil solarization. However, these methods reduce nematodes primarily in the top foot or so of the soil, so they are effective only for about a year. They are suitable primarily for annual plants or to help young woody plants establish. Once nematodes infest an area or crop, try to minimize damage by adjusting planting dates to cooler times of the season when nematodes are less active. Try to provide optimal conditions for plant growth including sufficient irrigation and soil amendments to make plants more tolerant to nematode infestation.