Subgroups — #17984162

Order 4384.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14555513	C₂	1	2	yes	maximal, complemented
2	C₂×#11764040	C₂	1	1	yes	maximal, characteristic
3	#11764040	C₄	1	1	yes	characteristic
4	#11764040	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₁₃₇	C₄	1	1	yes	characteristic
6	C₂²×C₁₃₇	C₈	1	1	yes	characteristic
7	C₄×C₁₃₇	C₈	1	1	yes	characteristic
8	C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
9	C₂×C₁₃₇	—	2	1	no	—
10	C₂×C₁₃₇	C₂×C₈	1	1	yes	characteristic
11	C₁₃₇	M₃₂	1	1	yes	characteristic, complemented, Sylow
12	M₃₂	—	137	1	no	maximal, Sylow
13	C₂×C₈	—	137	1	no	—
14	C₁₆	—	137	2	no	—
15	C₂×C₄	#10587739	1	1	yes	characteristic
16	C₈	—	137	1	no	—
17	C₈	—	137	1	no	—
18	C₂²	#11764047	1	1	yes	characteristic
19	C₄	#11764047	1	1	yes	characteristic
20	C₄	C₂×#10587739	1	1	yes	characteristic
21	C₂	—	2	1	no	—
22	C₂	C₂×#11764047	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #14555513	C₂	semidirect
11. C₁₃₇	M₃₂	semidirect

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