| 6T1 |
$C_6$ |
6 |
-1 |
Yes |
$C_2$, $C_3$ |
|
| 6T2 |
$S_3$ |
6 |
-1 |
Yes |
$C_2$, $S_3$ |
3T2 |
| 6T3 |
$D_{6}$ |
12 |
-1 |
Yes |
$C_2$, $S_3$ |
6T3, 12T3 |
| 6T4 |
$A_4$ |
12 |
1 |
Yes |
$C_3$ |
4T4, 12T4 |
| 6T5 |
$S_3\times C_3$ |
18 |
-1 |
Yes |
$C_2$ |
9T4, 18T3 |
| 6T6 |
$A_4\times C_2$ |
24 |
-1 |
Yes |
$C_3$ |
8T13, 12T6, 12T7, 24T9 |
| 6T7 |
$S_4$ |
24 |
1 |
Yes |
$S_3$ |
4T5, 6T8, 8T14, 12T8, 12T9, 24T10 |
| 6T8 |
$S_4$ |
24 |
-1 |
Yes |
$S_3$ |
4T5, 6T7, 8T14, 12T8, 12T9, 24T10 |
| 6T9 |
$S_3^2$ |
36 |
-1 |
Yes |
$C_2$ |
9T8, 12T16, 18T9, 18T11 x 2, 36T13 |
| 6T10 |
$C_3^2:C_4$ |
36 |
1 |
Yes |
$C_2$ |
6T10, 9T9, 12T17 x 2, 18T10, 36T14 |
| 6T11 |
$S_4\times C_2$ |
48 |
-1 |
Yes |
$S_3$ |
6T11, 8T24 x 2, 12T21, 12T22, 12T23 x 2, 12T24 x 2, 16T61, 24T46, 24T47, 24T48 x 2 |
| 6T12 |
$\PSL(2,5)$ |
60 |
1 |
No |
|
5T4, 10T7, 12T33, 15T5, 20T15, 30T9 |
| 6T13 |
$C_3^2:D_4$ |
72 |
-1 |
Yes |
$C_2$ |
6T13, 9T16, 12T34 x 2, 12T35 x 2, 12T36 x 2, 18T34 x 2, 18T36, 24T72 x 2, 36T53, 36T54 x 2 |
| 6T14 |
$\PGL(2,5)$ |
120 |
-1 |
No |
|
5T5, 10T12, 10T13, 12T74, 15T10, 20T30, 20T32, 20T35, 24T202, 30T22, 30T25, 30T27, 40T62 |
| 6T15 |
$A_6$ |
360 |
1 |
No |
|
6T15, 10T26, 15T20 x 2, 20T89, 30T88 x 2, 36T555, 40T304, 45T49 |
| 6T16 |
$S_6$ |
720 |
-1 |
No |
|
6T16, 10T32, 12T183 x 2, 15T28 x 2, 20T145, 20T149 x 2, 30T164 x 2, 30T166 x 2, 30T176 x 2, 36T1252, 40T589, 40T592 x 2, 45T96 |
