Subgroups — #14545888

Order 2176.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763891	C₂	1	2	yes	maximal, complemented
2	C₂×#10587467	C₂	1	1	yes	maximal, characteristic
3	C₂×#63214	C₄	1	1	yes	characteristic
4	#10587467	C₄	1	1	yes	characteristic
5	#10587467	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₁₇	C₈	1	1	yes	characteristic
7	#63214	C₈	1	1	yes	characteristic
8	#63214	C₂×C₄	1	1	yes	characteristic
9	C₂×C₄×C₁₇	C₁₆	1	1	yes	characteristic
10	C₈×C₁₇	C₁₆	1	1	yes	characteristic
11	C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
12	M₁₂₈	—	17	1	no	maximal, Sylow
13	C₂²×C₁₇	C₃₂	1	1	yes	characteristic
14	C₄×C₁₇	C₃₂	1	1	yes	characteristic
15	C₄×C₁₇	C₂×C₁₆	1	1	yes	characteristic
16	C₂×C₃₂	—	17	1	no	—
17	C₆₄	—	17	2	no	—
18	C₂×C₁₇	—	2	1	no	—
19	C₂×C₁₇	C₂×C₃₂	1	1	yes	characteristic
20	C₂×C₁₆	—	17	1	no	—
21	C₃₂	—	17	1	no	—
22	C₃₂	—	17	1	no	—
23	C₁₇	M₁₂₈	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₈	#3633	1	1	yes	characteristic
25	C₁₆	—	17	1	no	—
26	C₁₆	—	17	1	no	—
27	C₂×C₄	#63241	1	1	yes	characteristic
28	C₈	#63241	1	1	yes	characteristic
29	C₈	C₂×#3633	1	1	yes	characteristic
30	C₂²	#10587528	1	1	yes	characteristic
31	C₄	#10587528	1	1	yes	characteristic
32	C₄	C₂×#63241	1	1	yes	characteristic
33	C₂	—	2	1	no	—
34	C₂	C₂×#10587528	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #11763891	C₂	semidirect
23. C₁₇	M₁₂₈	semidirect

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