Distribution of groups in curves of genus 3

Isomorphism class GAP/Magma Group Distinct generating vectors
$C_2$ [2,1] 1
$C_3$ [3,1] 2
$C_4$ [4,1] 5
$C_2^2$ [4,2] 7
$S_3$ [6,1] 9
$C_6$ [6,2] 3
$C_7$ [7,1] 8
$C_8$ [8,1] 6
$C_2\times C_4$ [8,2] 12
$D_4$ [8,3] 6
$C_2^3$ [8,5] 28
$C_9$ [9,1] 6
$C_3:C_4$ [12,1] 2
$C_{12}$ [12,2] 6
$A_4$ [12,3] 3
$D_6$ [12,4] 2
$C_{14}$ [14,2] 6
$C_4^2$ [16,2] 16
$C_4:C_4$ [16,4] 4
$C_2\times C_8$ [16,5] 8
$OD_{16}$ [16,6] 2
$C_2\times D_4$ [16,11] 8
$D_4:C_2$ [16,13] 2
$C_7:C_3$ [21,1] 2
$\SL(2,3)$ [24,3] 2
$C_4\times S_3$ [24,5] 4
$S_4$ [24,12] 4
$C_2\times A_4$ [24,13] 1
$D_4:C_4$ [32,9] 8
$C_4\wr C_2$ [32,11] 4
$C_4^2:C_3$ [48,3] 4
$\SL(2,3):C_2$ [48,33] 4
$C_2\times S_4$ [48,48] 2
$C_4^2:C_3:C_2$ [96,64] 2
$\PSL(2,7)$ [168,42] 2