Distribution of groups in curves of genus 8

Isomorphism class GAP/Magma Group Distinct generating vectors
$C_2$ [2,1] 1
$C_3$ [3,1] 3
$C_4$ [4,1] 6
$C_2^2$ [4,2] 15
$C_5$ [5,1] 16
$S_3$ [6,1] 178
$C_6$ [6,2] 17
$C_8$ [8,1] 8
$D_4$ [8,3] 61
$Q_8$ [8,4] 13
$C_9$ [9,1] 12
$D_5$ [10,1] 16
$C_{10}$ [10,2] 24
$C_3:C_4$ [12,1] 3
$C_{12}$ [12,2] 11
$A_4$ [12,3] 16
$D_6$ [12,4] 25
$C_2\times C_6$ [12,5] 33
$D_7$ [14,1] 1200
$C_{15}$ [15,1] 2
$C_{16}$ [16,1] 4
$D_8$ [16,7] 66
$SD_{16}$ [16,8] 4
$Q_{16}$ [16,9] 2
$C_{17}$ [17,1] 48
$D_9$ [18,1] 12
$C_{18}$ [18,2] 15
$C_{20}$ [20,2] 12
$D_{10}$ [20,4] 8
$C_2\times C_{10}$ [20,5] 24
$C_7:C_3$ [21,1] 16
$C_3:C_8$ [24,1] 2
$C_{24}$ [24,2] 4
$\SL(2,3)$ [24,3] 1
$D_{12}$ [24,6] 6
$C_3:D_4$ [24,8] 4
$C_3\times D_4$ [24,10] 4
$C_3\times Q_8$ [24,11] 6
$S_4$ [24,12] 8
$D_{14}$ [28,3] 48
$C_5\times S_3$ [30,1] 2
$C_3\times D_5$ [30,2] 2
$D_{15}$ [30,3] 4
$C_{32}$ [32,1] 8
$D_{16}$ [32,18] 4
$Q_{32}$ [32,20] 4
$C_{34}$ [34,2] 16
$C_9:C_4$ [36,1] 3
$D_{18}$ [36,4] 3
$C_2\times C_{18}$ [36,5] 18
$C_5\times D_4$ [40,10] 8
$F_7$ [42,1] 10
$C_2\times C_7:C_3$ [42,2] 4
$Q_8:S_3$ [48,17] 4
$C_3\times D_8$ [48,25] 8
$C_2.S_4$ [48,28] 2
$S_3\times D_5$ [60,8] 2
$SD_{64}$ [64,53] 8
$C_9:D_4$ [72,8] 6
$C_2\times F_7$ [84,7] 4
$\PSL(2,7)$ [168,42] 4
$SO(3,7)$ [336,208] 2