Geomagnetic indices are used to measure the intensity of geomagnetic storms. In the study of solar terrestrial relationship the use of indices of geo magnetic activity plays an important role. The aim of this work is to compare the linear relationship between geomagnetic indices at quiet and disturbed period when ap <26nTand ap > 26nT for solar maximum in the year (2001). Auroral indices obtained from the omni-web are compared for the geomagnetic disturbance of different intensities. Three hourly average values of the Dst, ap, AE and Bz indices have been studied for one year of high solar activity (2001) during quiet and disturbed period. Thus, the correlations of geomagnetic indices were determined by plotting graphs of the indices against one another. The study reveals that the annual correlation coefficient of AE×ap is 72.3% for quiet period, which is the highest correlation. Also, the coefficient of Dst ×Bz is 7.94% for quiet period, which is the least correlation. For the monthly correlation, the correlation coefficient of AE× Bz in the month of May is 84.9% for disturbed period, which is the highest correlation. Also, the correlation coefficient of ap× Dst in the month of January is 1% for disturbed period, which is the least correlation. For both annual and monthly coefficient, the correlation coefficient of AE × ap (3-hourly values) for quiet period is in general the highest of all, followed by AE × Bz for disturbed and quiet period. Thus, ap is strongly influenced by AE activity or ap is the major factor that determines the auroral activity. It is observed that when Bz has values within -10nT and lower the auroral activities (AE) increases and gives a better correlation relatively to other geomagnetic indices. Also, it is observed that there was intense (or strong) storm in the months of April and October for both disturbed and quiet period. Thus, these months (April and October) could be seen as a critical months which must be given a special attention for consideration in the further studies.