An industry trade group's manufacturing index slipped in June, but was still at a level that suggests growth in the industrial sector. The manufacturing sector has been one of the US economy's bright spots for nearly a year as companies restock inventories and replace old equipment. As the initial burst of activity for companies coming out of a deep decline during the recession drops off, economic growth will slow, analysts say - especially if consumer spending remains weak. The Institute for Supply Management said Thursday its index fell to 56.2 last month from 59.7 in May. That was a steeper drop than economists expected. They were looking for a reading 59 for last month, according to a survey by Thomson Reuters. A reading above 50 indicates expansion. “The problem in the current recovery is that it has largely been concentrated in the manufacturing sector and if growth in the sector slows, and it is, then there is no sector ready to take the growth baton,” said Dan Greenhaus, chief economic strategist of Miller Tabak. The Commerce Department said last week that the economy grew at an annual rate of 2.7 percent in the first quarter. Slower growth in manufacturing suggests the broader economy is going to be more “subdued” for the rest of 2010, said Alistair Bentley a research analyst. The economic momentum is also slowing worldwide. Surveys released Thursday in China showed a slowdown in factories' growth as exports faltered and analysts worry that cutbacks in government lending will cool the economy's rapid rise. Reports from Markit Economics also indicated that manufacturing sector growth in India, South Korea, Australia and Taiwan was slowing. The industrial sector's growth also cooled slightly in the 16 countries using the euro and the United Kingdom. ISM's report showed that in the US, new orders and production are not growing as fast as they had been. Strength in new orders, which signal future production, hit a five