Automatically shiftable motor vehicle transmission

An automatically shiftable motor vehicle transmission of planetary design for a motor vehicle, comprising:

• an input drive shaft (1) and an output drive shaft (2) that are arranged in a housing (G);
• first, second and third single-carrier planetary gear sets (P1, P2, P3);
• third, fourth, fifth and sixth rotatable shafts (3, 4, 5, 6);
• a plurality of shifting elements comprising first, second and third brakes (03, 04, 05), and first, second, and third clutches (14, 15, 45) selective engagement of which brings about various conversion ratios between the input drive shaft (1) and output drive shaft (2), so that at least seven forward speeds can be implemented;
• the input drive shaft (1) being continuously connected to a sun gear of the second planetary gear set (P2) and being connectable via the first clutch (14) to a carrier of the first planetary gear set (P1) and being connectable via the second clutch (15) to the fifth shaft (5) which is continuously connected to a sun gear of the first planetary gear set (P1) and is couplable via the third brake (05) to the housing (G);
• the output drive shaft (2) being continuously connected to a carrier of the third planetary gear set (P3) and to the ring gear of the first planetary gear set (P1);
• the third shaft (3) being continuously connected to a sun gear of the third planetary gear set (P3) and being couplable by way of the first brake (03) to the housing (G);
• the fourth shaft (4) being continuously connected to a ring gear of the second planetary gear set (P2) and to the carrier of the first planetary gear set (P1), and being directly couplable to the housing (G) through only the second brake (04);
• the sixth shaft (6) being continuously connected to a ring gear of the third planetary gear set (P3) and to a carrier of the second planetary gear set (P2);
• and
• the third clutch (45) being provided which releasably connects the fourth shaft (4) to one of the fifth shaft (5) and the output drive shaft (2).