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From about halfway down this page on the CRA of '64:
Of the 420 members who voted, 290 supported the civil rights bill and 130 opposed it. Republicans favored the bill 138 to 34 (80%); Democrats supported it 152-96 (61%).

From further down on the same page:
The Republican Party was not so badly split as the Democrats by the civil rights issue. Only one Republican senator participated in the filibuster against the bill. In fact, since 1933, Republicans had a more positive record on civil rights than the Democrats. In the twenty-six major civil rights votes since 1933, a majority of Democrats opposed civil rights legislation in over 80 % of the votes. By contrast, the Republican majority favored civil rights in over 96 % of the votes.
The Republican pro-civil rights forces were blessed with gifted leadership. Although Senate minority whip Thomas Kuchel initially managed the party's forces, it increasingly became clear to Democrats, Republicans, the press, civil rights groups, and the White House that Everett McKinley Dirksen was the key man in the entire civil rights legislative effort.

The bill was filibustered in the Senate by 17 Democrats and one Republican. The final vote for cloture was 71-29, Republicans 27-6 (82%), Democrats 44-23 (66%). The actual vote - again from the same source:
...Two days later, the Senate passed the bill by a 73 to 27 roll call vote. Six Republicans and 21 Democrats held firm and voted against passage.
That would be of 33 and 67 respectively, meaning 18% R and 31% D against the Civil Rights Act. Now I know.