T	Name(s)	\|G\|	Parity	\|C_S₁₄(G)\|	Subfields	Other Representations	Resolvents
1	C(14)=7[x]2	14 = 2 · 7	-1	14	2T1, 7T1		2: 2T1 7: 7T1
2	D_14(14)=[7]2	14 = 2 · 7	-1	14	2T1, 7T2	7T2	2: 2T1
3	D(7)[x]2	28 = 2² · 7	-1	2	2T1, 7T2	14T3	2: 2T1, 2T1, 2T1 4: 4T2 14: 7T2
4	2[1/2]F_42(7)	42 = 2 · 3 · 7	-1	2	2T1, 7T4	7T4, 21T4	2: 2T1 3: 3T1 6: 6T1
5	F_21(7)[x]2	42 = 2 · 3 · 7	-1	2	2T1, 7T3		2: 2T1 3: 3T1 6: 6T1 21: 7T3
6	[2^3]7	56 = 2³ · 7	1	2	7T1	8T25	7: 7T1
7	F_42(7)[x]2	84 = 2² · 3 · 7	-1	2	2T1, 7T4	14T7	2: 2T1, 2T1, 2T1 3: 3T1 4: 4T2 6: 6T1, 6T1, 6T1 12: 12T2 42: 7T4
8	[7^2]2=7wr2	98 = 2 · 7²	-1	7	2T1	14T8, 14T8	2: 2T1 7: 7T1 14: 7T2, 14T1
9	[2^4]7	112 = 2⁴ · 7	-1	2	7T1	16T196	2: 2T1 7: 7T1 14: 14T1 56: 8T25
10	L_7(14)	168 = 2³ · 3 · 7	1	2	7T5	7T5, 7T5, 8T37, 14T10, 21T14
11	[2^3]F_21(7)	168 = 2³ · 3 · 7	1	2	7T3	8T36	3: 3T1 21: 7T3
12	1/2[D(7)^2]2	196 = 2² · 7²	1	1	2T1	14T12, 14T12, 14T12	2: 2T1 4: 4T1
13	[1/2.D(7)^2]2	196 = 2² · 7²	-1	1	2T1	14T13, 14T13	2: 2T1, 2T1, 2T1 4: 4T2 14: 7T2, 7T2 28: 14T3, 14T3
14	[7^2:3]2	294 = 2 · 3 · 7²	-1	1	2T1	14T14, 14T14	2: 2T1 3: 3T1 6: 6T1 21: 7T3 42: 7T4, 14T5
15	[7^2:3_3]2	294 = 2 · 3 · 7²	-1	1	2T1	21T18, 21T17	2: 2T1 6: 3T2
16	L_7:2(14)=[L(7)_%]2	336 = 2⁴ · 3 · 7	-1	1	2T1	8T43, 16T713, 21T20	2: 2T1
17	2L_7(14)=[2]L(7)	336 = 2⁴ · 3 · 7	-1	2	7T5	14T19, 14T19, 14T17, 16T714	2: 2T1 168: 7T5
18	[2^4]F_21(7)	336 = 2⁴ · 3 · 7	-1	2	7T3	16T712	2: 2T1 3: 3T1 6: 6T1 21: 7T3 42: 14T5 168: 8T36
19	L(7)[x]2	336 = 2⁴ · 3 · 7	-1	2	2T1, 7T5	14T17, 14T19, 14T17, 16T714	2: 2T1 168: 7T5
20	[D(7)^2]2=D(7)wr2	392 = 2³ · 7²	-1	1	2T1	14T20	2: 2T1, 2T1, 2T1 4: 4T2 8: 4T3
21	[2^6]7	448 = 2⁶ · 7	1	2	7T1	14T21, 14T21, 14T21, 14T21, 14T21, 14T21	7: 7T1 56: 8T25, 8T25
22	[1/6_-.F_42(7)^2]2_2	588 = 2² · 3 · 7²	1	1	2T1		2: 2T1 4: 4T1 6: 3T2 12: 12T5
23	[1/6_+.F_42(7)^2]2_2	588 = 2² · 3 · 7²	1	1	2T1	14T23, 14T23, 14T23	2: 2T1 3: 3T1 4: 4T1 6: 6T1 12: 12T1
24	[7^2:6]2	588 = 2² · 3 · 7²	-1	1	2T1	14T24, 14T24	2: 2T1, 2T1, 2T1 3: 3T1 4: 4T2 6: 6T1, 6T1, 6T1 12: 12T2 42: 7T4, 7T4 84: 14T7, 14T7
25	[7^2:6_3]2	588 = 2² · 3 · 7²	-1	1	2T1	21T23, 21T23	2: 2T1, 2T1, 2T1 4: 4T2 6: 3T2 12: 6T3
26	1/2[1/2.F_42(7)^2]2	882 = 2 · 3² · 7²	-1	1	2T1	21T26, 21T25	2: 2T1 3: 3T1 6: 3T2, 6T1 18: 6T5
27	2^7[1/2]D(7)	896 = 2⁷ · 7	-1	2	7T2	14T28, 14T27, 14T28, 14T27, 14T28, 14T28, 14T27, 14T27, 14T28, 14T27, 14T28, 14T28, 14T27, 16T1078	2: 2T1 14: 7T2
28	[2^6]D(7)	896 = 2⁷ · 7	1	2	7T2	14T27, 14T28, 14T27, 14T28, 14T27, 14T28, 14T27, 14T28, 14T27, 14T28, 14T27, 14T28, 14T27, 16T1078	2: 2T1 14: 7T2
29	[2^7]7=2wr7	896 = 2⁷ · 7	-1	2	7T1	14T29, 14T29, 14T29, 14T29, 14T29, 14T29	2: 2T1 7: 7T1 14: 14T1 56: 8T25, 8T25 112: 14T9, 14T9 448: 14T21
30	L(14)=PSL(2,13)	1092 = 2² · 3 · 7 · 13	1	1
31	[D(7)^2:3_3]2	1176 = 2³ · 3 · 7²	-1	1	2T1		2: 2T1, 2T1, 2T1 4: 4T2 6: 3T2 8: 4T3 12: 6T3 24: 12T13
32	[D(7)^2:3]2	1176 = 2³ · 3 · 7²	-1	1	2T1	14T32	2: 2T1, 2T1, 2T1 3: 3T1 4: 4T2 6: 6T1, 6T1, 6T1 8: 4T3 12: 12T2 24: 12T14
33	2^3`L_7(14)	1344 = 2⁶ · 3 · 7	1	2	7T5	14T33	168: 7T5
34	2^3:L_7(14)=[2^3]L(7)=[2^3]L(3,2)	1344 = 2⁶ · 3 · 7	1	2	7T5	8T48, 8T48, 14T34	168: 7T5
35	[2^6]F_21(7)	1344 = 2⁶ · 3 · 7	1	2	7T3		3: 3T1 21: 7T3 168: 8T36, 8T36
36	1/2[F_42(7)^2]2	1764 = 2² · 3² · 7²	1	1	2T1		2: 2T1 3: 3T1 4: 4T1 6: 3T2, 6T1 12: 12T1, 12T5 18: 6T5 36: 12T19
37	[1/2.F_42(7)^2]2	1764 = 2² · 3² · 7²	-1	1	2T1	21T29, 21T29	2: 2T1, 2T1, 2T1 3: 3T1 4: 4T2 6: 3T2, 6T1, 6T1, 6T1 12: 6T3, 12T2 18: 6T5 36: 12T18
38	[2^7]D(7)=2wrD(7)	1792 = 2⁸ · 7	-1	2	7T2	14T38, 14T38, 14T38, 14T38, 14T38, 14T38, 14T38, 14T38, 14T38, 14T38, 14T38, 14T38, 14T38	2: 2T1, 2T1, 2T1 4: 4T2 14: 7T2 28: 14T3 896: 14T27
39	L(14):2=PGL(2,13)	2184 = 2³ · 3 · 7 · 13	-1	1			2: 2T1
40	1/2[2^7]F_42(7)	2688 = 2⁷ · 3 · 7	-1	2	7T4	14T41, 16T1502	2: 2T1 3: 3T1 6: 6T1 42: 7T4
41	[2^6]F_42(7)	2688 = 2⁷ · 3 · 7	1	2	7T4	14T40, 16T1502	2: 2T1 3: 3T1 6: 6T1 42: 7T4
42	2^4`L_7(14)	2688 = 2⁷ · 3 · 7	-1	2	7T5	14T42	2: 2T1 168: 7T5 336: 14T17 1344: 14T33
43	2^4:L_7(14)=[2^4]L(7)	2688 = 2⁷ · 3 · 7	-1	2	7T5	14T43, 16T1504, 16T1504	2: 2T1 168: 7T5 336: 14T17 1344: 8T48
44	[2^7]F_21(7)=2wrF_21(7)	2688 = 2⁷ · 3 · 7	-1	2	7T3		2: 2T1 3: 3T1 6: 6T1 21: 7T3 42: 14T5 168: 8T36, 8T36 336: 14T18, 14T18 1344: 14T35
45	[F_42(7)^2]2=F_42(7)wr2	3528 = 2³ · 3² · 7²	-1	1	2T1		2: 2T1, 2T1, 2T1 3: 3T1 4: 4T2 6: 3T2, 6T1, 6T1, 6T1 8: 4T3 12: 6T3, 12T2 18: 6T5 24: 12T13, 12T14 36: 12T18 72: 12T42
46	2[1/2]S(7)	5040 = 2⁴ · 3² · 5 · 7	-1	2	2T1, 7T7	7T7, 21T38	2: 2T1
47	2[x]A(7)	5040 = 2⁴ · 3² · 5 · 7	-1	2	2T1, 7T6		2: 2T1 2520: 7T6
48	[2^7]F_42(7)=2wrF_42(7)	5376 = 2⁸ · 3 · 7	-1	2	7T4	14T48	2: 2T1, 2T1, 2T1 3: 3T1 4: 4T2 6: 6T1, 6T1, 6T1 12: 12T2 42: 7T4 84: 14T7 2688: 14T40
49	2[x]S(7)	10080 = 2⁵ · 3² · 5 · 7	-1	2	2T1, 7T7	14T49	2: 2T1, 2T1, 2T1 4: 4T2 5040: 7T7
50	[2^6]L(7)	10752 = 2⁹ · 3 · 7	1	2	7T5	14T50	168: 7T5 1344: 8T48
51	[2^7]L(7)=2wrL(7)	21504 = 2¹⁰ · 3 · 7	-1	2	7T5	14T51	2: 2T1 168: 7T5 336: 14T17 1344: 8T48 2688: 14T43 10752: 14T50
52	[L(7)^2]2=L(7)wr2	56448 = 2⁷ · 3² · 7²	-1	1	2T1	14T52, 16T1861	2: 2T1
53	[2^6]A(7)	161280 = 2⁹ · 3² · 5 · 7	1	2	7T6		2520: 7T6
54	1/2[2^7]S(7)	322560 = 2¹⁰ · 3² · 5 · 7	-1	2	7T7	14T55	2: 2T1 5040: 7T7
55	[2^6]S(7)	322560 = 2¹⁰ · 3² · 5 · 7	1	2	7T7	14T54	2: 2T1 5040: 7T7
56	[2^7]A(7)=2wrA(7)	322560 = 2¹⁰ · 3² · 5 · 7	-1	2	7T6		2: 2T1 2520: 7T6 5040: 14T47 161280: 14T53
57	[2^7]S(7)	645120 = 2¹¹ · 3² · 5 · 7	-1	2	7T7	14T57	2: 2T1, 2T1, 2T1 4: 4T2 5040: 7T7 10080: 14T49 322560: 14T54
58	[A(7)^2]2=A(7)wr2	12700800 = 2⁷ · 3⁴ · 5² · 7²	-1	1	2T1		2: 2T1
59	1/2[S(7)^2]2	25401600 = 2⁸ · 3⁴ · 5² · 7²	1	1	2T1		2: 2T1 4: 4T1
60	[1/2.S(7)^2]2	25401600 = 2⁸ · 3⁴ · 5² · 7²	-1	1	2T1		2: 2T1, 2T1, 2T1 4: 4T2
61	[S(7)^2]2=S(7)wr2	50803200 = 2⁹ · 3⁴ · 5² · 7²	-1	1	2T1		2: 2T1, 2T1, 2T1 4: 4T2 8: 4T3
62	A14	43589145600 = 2¹⁰ · 3⁵ · 5² · 7² · 11 · 13	1	1
63	S14	87178291200 = 2¹¹ · 3⁵ · 5² · 7² · 11 · 13	-1	1			2: 2T1

Transitive Subgroups of S14

Transitive Subgroups of S₁₄