Subgroups — #31797894

Order 17536.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22578485	C₂	1	2	yes	maximal, complemented
2	#22578334	C₂	1	1	yes	maximal, characteristic
3	#17984138	C₄	1	1	yes	characteristic
4	#17984138	C₂²	1	1	yes	characteristic
5	C₁₆×D₁₃₇	C₄	1	1	yes	characteristic
6	C₈×D₁₃₇	C₈	1	1	yes	characteristic
7	#14555485	C₂×C₄	1	1	yes	characteristic
8	C₁₆×C₁₃₇	C₈	1	1	yes	characteristic
9	C₄×D₁₃₇	C₁₆	1	1	yes	characteristic
10	#11764040	C₁₆	1	1	yes	characteristic
11	C₈×C₁₃₇	C₂×C₈	1	1	yes	characteristic
12	C₂×D₁₃₇	C₃₂	1	1	yes	characteristic
13	C₄×C₁₃₇	C₂×C₁₆	1	1	yes	characteristic
14	Dic₁₃₇	C₃₂	1	1	yes	characteristic
15	C₂×C₁₃₇	C₂×C₃₂	1	1	yes	characteristic
16	D₁₃₇	—	2	1	no	—
17	C₁₃₇	M₁₂₈	1	1	yes	characteristic, complemented, Sylow
18	M₁₂₈	—	137	1	no	maximal, Sylow
19	C₂×C₃₂	—	137	1	no	—
20	C₆₄	—	137	2	no	—
21	C₂×C₁₆	—	137	1	no	—
22	C₃₂	—	137	1	no	—
23	C₃₂	—	137	1	no	—
24	C₂×C₈	—	137	1	no	—
25	C₁₆	—	137	1	no	—
26	C₁₆	#11764049	1	1	yes	characteristic
27	C₂×C₄	—	137	1	no	—
28	C₈	—	137	1	no	—
29	C₈	C₂×#11764049	1	1	yes	characteristic
30	C₂²	—	137	1	no	—
31	C₄	—	137	1	no	—
32	C₄	#17984183	1	1	yes	characteristic
33	C₂	—	274	1	no	—
34	C₂	#22578510	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #22578485	C₂	semidirect
17. C₁₃₇	M₁₂₈	semidirect

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