Subgroups — #36342167

Order 21568.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#14582113	C₂	1	2	yes	maximal
2	C₈×Dic₃₃₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582113	—	2	2	no	—
4	C₂×#14582106	C₄	1	1	yes	characteristic
5	C₄×Dic₃₃₇	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₃₃₇	C₄	1	1	yes	characteristic
7	#14582113	—	4	2	no	—
8	C₂×Dic₃₃₇	D₄	1	1	yes	characteristic
9	C₂×Dic₃₃₇	Q₈	1	1	yes	characteristic
10	#14582106	C₈	1	2	yes	complemented
11	C₂×C₄×C₃₃₇	C₂×C₄	1	1	yes	characteristic
12	C₈×C₃₃₇	—	2	1	no	—
13	C₂²×C₃₃₇	C₄⋊C₄	1	1	yes	characteristic
14	C₄×C₃₃₇	C₂×C₈	1	1	yes	characteristic
15	C₄×C₃₃₇	M₁₆	1	1	yes	characteristic
16	Dic₃₃₇	—	2	1	no	—
17	Dic₃₃₇	SD₁₆	1	2	yes	—
18	C₂×C₃₃₇	C₄⋊C₈	1	1	yes	characteristic
19	C₂×C₃₃₇	#106	1	1	yes	characteristic
20	C₂×C₃₃₇	#108	1	1	yes	characteristic
21	C₃₃₇	#334	1	1	yes	characteristic, complemented, Sylow
22	#334	—	337	1	no	maximal, Sylow
23	C₄⋊C₈	—	337	2	no	—
24	C₄×C₈	—	337	1	no	—
25	C₂×C₈	—	337	1	no	—
26	C₂×C₈	—	674	2	no	—
27	C₂×C₈	#13062438	1	1	yes	characteristic
28	C₄²	—	337	1	no	—
29	C₂×C₄	—	337	1	no	—
30	C₂×C₄	—	337	1	no	—
31	C₂×C₄	C₂×#13062438	1	1	yes	characteristic
32	C₈	—	2	1	no	—
33	C₈	—	1348	2	no	—
34	C₈	—	337	2	no	—
35	C₂²	C₄⋊#13062438	1	1	yes	characteristic
36	C₄	—	337	2	no	—
37	C₄	—	674	1	no	—
38	C₄	#19129193	1	1	yes	characteristic
39	C₄	#19129194	1	1	yes	characteristic
40	C₂	#24925026	1	1	yes	characteristic
41	C₂	#24925027	1	1	yes	characteristic
42	C₂	#24925030	1	1	yes	characteristic

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

N	H ≅ G/N	type
10. #14582106	C₈	semidirect
21. C₃₃₇	#334	semidirect

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