Subgroups — #24925056

Order 10784.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19129197	C₂	1	2	yes	maximal, complemented
2	#19129193	C₂	1	1	yes	maximal, characteristic
3	#14582113	C₄	1	1	yes	characteristic
4	#14582113	C₂²	1	1	yes	characteristic
5	C₄×D₃₃₇	C₄	1	1	yes	characteristic
6	C₂×D₃₃₇	C₈	1	1	yes	characteristic
7	C₄×C₃₃₇	C₈	1	1	yes	characteristic
8	Dic₃₃₇	C₂×C₄	1	1	yes	characteristic
9	C₂×C₃₃₇	C₂×C₈	1	1	yes	characteristic
10	D₃₃₇	—	2	1	no	—
11	C₃₃₇	M₃₂	1	1	yes	characteristic, complemented, Sylow
12	M₃₂	—	337	1	no	maximal, Sylow
13	C₂×C₈	—	337	1	no	—
14	C₁₆	—	337	2	no	—
15	C₂×C₄	—	337	1	no	—
16	C₈	—	337	1	no	—
17	C₈	—	337	1	no	—
18	C₂²	—	337	1	no	—
19	C₄	—	337	1	no	—
20	C₄	#14582115	1	1	yes	characteristic
21	C₂	—	674	1	no	—
22	C₂	C₂×#14582115	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #19129197	C₂	semidirect
11. C₃₃₇	M₃₂	semidirect