1. A search device comprising: a first storage configured to store therein keyword candidates for a search keyword in advance; an input unit configured to receive an input operation of a character string by a user; a first acquisition unit configured to acquire first recommended keywords each of which is a keyword candidate including an input character string, the input character string being a character string which is partially entered by the user as the search keyword; and a search unit configured to select one of the acquired first recommended keywords selected on a search screen as the search keyword to perform a search with the search keyword; an output unit configured to output a search result on the search screen, wherein the search device further comprises, a second storage configured to store therein keyword candidates in association with keyword groups, the keyword groups grouping the keyword candidates for a search keyword stored in the first storage according to a rule set in advance; a second acquisition unit configured to acquire second recommended keywords each of which is a keyword candidate included in a keyword group to which an acquired first recommended keyword belongs and which is the keyword candidate other than the acquired first recommended keyword, wherein when the first acquisition unit acquires a plurality of first recommended keywords each of which includes the input character string, the second acquisition unit selects, among keyword groups to which at least one of the acquired first recommended keywords belongs, a predetermined number of the keyword groups in a descending order of the number of the acquired first recommended keywords belonging thereto, and acquires, as the second recommended keywords, the keyword candidates included in the selected keyword groups, and the search unit configured to sequentially select one of the acquired first recommended keywords and the acquired second recommended keywords on the search screen to perform a search with the sequentially selected one while the input character string is not repeatedly inputted.
5. The search device according to claim 1 , further comprising: a third storage configured to store therein history information indicating history of a search keyword used for a search by the search unit, wherein the second acquisition unit decides, based on the history information, the second recommended keywords to be acquired and an order of the second recommended keywords to be displayed on the search screen.