Subgroups — #36342399

Order 21568.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19129197	C₂	1	2	yes	maximal
2	C₄×#14582113	C₂	1	1	yes	maximal, characteristic
3	#19129197	C₄	1	4	yes	complemented
4	C₂×#14582113	C₄	1	1	yes	characteristic
5	C₂×#14582113	C₂²	1	1	yes	characteristic
6	C₄×Dic₃₃₇	C₄	1	1	yes	characteristic
7	#14582113	C₈	1	2	yes	—
8	#14582113	C₂×C₄	1	2	yes	—
9	C₂×Dic₃₃₇	C₈	1	1	yes	characteristic
10	C₂×Dic₃₃₇	C₂×C₄	1	1	yes	characteristic
11	C₂×C₄×C₃₃₇	C₈	1	1	yes	characteristic
12	C₂²×C₃₃₇	C₂×C₈	1	1	yes	characteristic
13	C₄×C₃₃₇	—	2	1	no	—
14	Dic₃₃₇	—	2	1	no	—
15	Dic₃₃₇	C₄²	1	1	yes	characteristic
16	Dic₃₃₇	C₂×C₈	1	1	yes	characteristic
17	C₂×C₃₃₇	C₄×C₈	1	1	yes	characteristic
18	C₂×C₃₃₇	M₃₂	1	1	yes	characteristic
19	C₂×C₃₃₇	M₃₂	1	1	yes	characteristic
20	C₃₃₇	#346	1	1	yes	characteristic, complemented, Sylow
21	#346	—	337	1	no	maximal, Sylow
22	C₂×C₁₆	—	337	2	no	—
23	C₄×C₈	—	337	1	no	—
24	C₂×C₈	—	337	1	no	—
25	C₂×C₈	—	337	1	no	—
26	C₄²	—	337	1	no	—
27	C₁₆	—	337	4	no	—
28	C₂×C₄	—	337	1	no	—
29	C₂×C₄	—	337	1	no	—
30	C₂×C₄	#14582115	1	1	yes	characteristic
31	C₈	—	337	2	no	—
32	C₈	—	337	2	no	—
33	C₂²	C₂×#14582115	1	1	yes	characteristic
34	C₄	—	2	1	no	—
35	C₄	—	337	1	no	—
36	C₄	—	337	1	no	—
37	C₄	—	674	1	no	—
38	C₂	C₄×#14582115	1	1	yes	characteristic
39	C₂	#24925055	1	1	yes	characteristic
40	C₂	#24925056	1	1	yes	characteristic

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

N	H ≅ G/N	type
3. #19129197	C₄	semidirect
20. C₃₃₇	#346	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.