Subgroups — #17981508

Order 4352.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14545782	C₂	1	2	yes	maximal, complemented
2	#14543952	C₂	1	1	yes	maximal, characteristic
3	#11763648	C₄	1	1	yes	characteristic
4	#11763648	C₂²	1	1	yes	characteristic
5	C₃₂×D₁₇	C₄	1	1	yes	characteristic
6	C₁₆×D₁₇	C₈	1	1	yes	characteristic
7	C₁₇×C₃₂	C₈	1	1	yes	characteristic
8	#10587465	C₂×C₄	1	1	yes	characteristic
9	C₈×D₁₇	C₁₆	1	1	yes	characteristic
10	C₁₆×C₁₇	C₂×C₈	1	1	yes	characteristic
11	#63214	C₁₆	1	1	yes	characteristic
12	M₂₅₆	—	17	1	no	maximal, Sylow
13	C₄×D₁₇	C₃₂	1	1	yes	characteristic
14	C₈×C₁₇	C₂×C₁₆	1	1	yes	characteristic
15	#3622	C₃₂	1	1	yes	characteristic
16	C₂×C₆₄	—	17	1	no	—
17	C₁₂₈	—	17	2	no	—
18	C₂×D₁₇	C₆₄	1	1	yes	characteristic
19	C₄×C₁₇	C₂×C₃₂	1	1	yes	characteristic
20	Dic₁₇	C₆₄	1	1	yes	characteristic
21	C₂×C₃₂	—	17	1	no	—
22	C₆₄	—	17	1	no	—
23	C₆₄	—	17	1	no	—
24	C₂×C₁₇	C₂×C₆₄	1	1	yes	characteristic
25	D₁₇	—	2	1	no	—
26	C₂×C₁₆	—	17	1	no	—
27	C₃₂	—	17	1	no	—
28	C₃₂	#3633	1	1	yes	characteristic
29	C₁₇	M₂₅₆	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₈	—	17	1	no	—
31	C₁₆	—	17	1	no	—
32	C₁₆	C₂×#3633	1	1	yes	characteristic
33	C₂×C₄	—	17	1	no	—
34	C₈	—	17	1	no	—
35	C₈	#10587665	1	1	yes	characteristic
36	C₂²	—	17	1	no	—
37	C₄	—	17	1	no	—
38	C₄	#11763916	1	1	yes	characteristic
39	C₂	—	34	1	no	—
40	C₂	#14545887	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #14545782	C₂	semidirect
29. C₁₇	M₂₅₆	semidirect

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