Subgroups — #22588485

Order 9088.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17985754	C₂	1	6	yes	maximal
2	#376×C₇₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₇₁⋊C₈	C₂²	1	4	yes	—
4	C₂×C₄²×C₇₁	C₂²	1	3	yes	—
5	#95×C₇₁	C₄	1	4	yes	—
6	C₂×C₇₁⋊C₈	—	2	12	no	—
7	C₂²×C₄×C₇₁	C₂×C₄	1	6	yes	—
8	C₂²×C₄×C₇₁	C₂³	1	1	yes	characteristic
9	C₄²×C₇₁	—	2	6	no	—
10	C₂³×C₇₁	C₂²×C₄	1	1	yes	characteristic
11	C₂×C₄×C₇₁	—	2	6	no	—
12	C₂×C₄×C₇₁	—	2	12	no	—
13	C₂×C₄×C₇₁	#41	1	6	yes	—
14	C₇₁⋊C₈	—	4	4	no	—
15	C₂²×C₇₁	#117	1	3	yes	—
16	C₂²×C₇₁	#131	1	4	yes	—
17	C₄×C₇₁	—	4	6	no	—
18	C₄×C₇₁	#126	1	4	yes	—
19	C₂×C₇₁	#383	1	1	yes	characteristic
20	C₂×C₇₁	#433	1	6	yes	—
21	#1840	—	71	1	no	maximal, Sylow
22	C₇₁	#1840	1	1	yes	characteristic, complemented, Sylow
23	#376	D₇₁	1	1	yes	characteristic
24	#336	—	71	6	no	—
25	C₂²×C₈	—	71	4	no	—
26	C₂×C₄²	C₂×D₇₁	1	3	yes	—
27	#95	Dic₇₁	1	4	yes	—
28	C₂²×C₄	C₂×Dic₇₁	1	6	yes	—
29	C₂²×C₄	C₂²×D₇₁	1	1	yes	characteristic
30	C₂×C₈	—	142	12	no	—
31	C₄²	—	2	6	no	—
32	C₂³	C₂²×Dic₇₁	1	1	yes	characteristic
33	C₂×C₄	—	2	6	no	—
34	C₂×C₄	—	2	12	no	—
35	C₂×C₄	#11765865	1	6	yes	—
36	C₈	—	284	4	no	—
37	C₂²	#14556087	1	3	yes	—
38	C₂²	#14556135	1	4	yes	—
39	C₄	—	4	6	no	—
40	C₄	#14556122	1	4	yes	—
41	C₂	#17985867	1	1	yes	characteristic
42	C₂	#17986060	1	6	yes	—

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
22. C₇₁	#1840	semidirect