Distribution of groups in curves of genus 14

Isomorphism class GAP/Magma Group Distinct generating vectors
$C_2$ [2,1] 1
$C_3$ [3,1] 5
$C_4$ [4,1] 15
$C_2^2$ [4,2] 36
$C_5$ [5,1] 44
$S_3$ [6,1] 14546
$C_6$ [6,2] 59
$C_8$ [8,1] 54
$D_4$ [8,3] 557
$Q_8$ [8,4] 109
$C_9$ [9,1] 36
$D_5$ [10,1] 3750
$C_{10}$ [10,2] 45
$C_3:C_4$ [12,1] 33
$C_{12}$ [12,2] 54
$A_4$ [12,3] 144
$D_6$ [12,4] 392
$C_2\times C_6$ [12,5] 148
$D_7$ [14,1] 7203
$C_{14}$ [14,2] 3
$C_{15}$ [15,1] 32
$C_{16}$ [16,1] 48
$D_8$ [16,7] 148
$SD_{16}$ [16,8] 74
$Q_{16}$ [16,9] 4
$D_9$ [18,1] 24
$C_{18}$ [18,2] 39
$C_5:C_4$ [20,1] 8
$C_{20}$ [20,2] 30
$F_5$ [20,3] 25
$D_{10}$ [20,4] 108
$C_2\times C_{10}$ [20,5] 42
$C_{21}$ [21,2] 12
$C_3:C_8$ [24,1] 6
$C_{24}$ [24,2] 6
$\SL(2,3)$ [24,3] 9
$C_3:Q_8$ [24,4] 6
$D_{12}$ [24,6] 10
$C_3:D_4$ [24,8] 88
$C_3\times D_4$ [24,10] 11
$C_3\times Q_8$ [24,11] 12
$S_4$ [24,12] 24
$D_{13}$ [26,1] 14280
$C_7:C_4$ [28,1] 3
$C_{28}$ [28,2] 6
$D_{14}$ [28,3] 297
$C_{29}$ [29,1] 140
$C_5\times S_3$ [30,1] 8
$C_3\times D_5$ [30,2] 8
$D_{15}$ [30,3] 20
$C_{30}$ [30,4] 20
$C_{32}$ [32,1] 32
$D_{16}$ [32,18] 16
$C_{35}$ [35,1] 36
$D_{18}$ [36,4] 6
$C_2\times C_{18}$ [36,5] 36
$C_{13}:C_3$ [39,1] 56
$C_5:C_8$ [40,1] 4
$C_{40}$ [40,2] 16
$C_{10}.C_4$ [40,3] 2
$D_{20}$ [40,6] 4
$C_5:D_4$ [40,8] 8
$C_5\times Q_8$ [40,11] 12
$C_3\times D_7$ [42,4] 12
$D_{21}$ [42,5] 12
$C_{42}$ [42,6] 6
$C_3:C_{16}$ [48,1] 4
$D_{24}$ [48,7] 4
$C_3:D_8$ [48,15] 4
$C_3:Q_{16}$ [48,18] 4
$C_3\times D_8$ [48,25] 4
$C_3\times SD_{16}$ [48,26] 4
$\GL(2,3)$ [48,29] 2
$D_{13}.C_2$ [52,3] 42
$D_{26}$ [52,4] 168
$C_{56}$ [56,2] 12
$C_7:Q_8$ [56,3] 6
$D_{28}$ [56,5] 6
$C_{58}$ [58,2] 28
$C_{15}:C_4$ [60,3] 4
$C_3:F_5$ [60,7] 2
$S_3\times D_5$ [60,8] 2
$D_{30}$ [60,12] 4
$C_2\times C_{30}$ [60,13] 24
$C_5\times D_7$ [70,2] 12
$D_{13}:C_3$ [78,1] 32
$C_2\times C_{13}:C_3$ [78,2] 8
$Q_8:D_5$ [80,17] 8
$C_6\times D_7$ [84,12] 12
$C_3:D_{16}$ [96,33] 8
$C_8:D_7$ [112,5] 12
$\SL(2,5)$ [120,5] 2
$D_{30}:C_2$ [120,30] 8
$C_2\times D_{13}:C_3$ [156,8] 8
$1092.25$ [1092,25] 6