Subgroups — #14543947

Order 2176.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763737	C₂	1	2	yes	maximal
2	C₃₂×D₁₇	C₂	1	1	yes	maximal, characteristic
3	#10587536	—	2	2	no	—
4	C₁₆×D₁₇	C₂²	1	1	yes	characteristic
5	C₁₇×C₃₂	C₄	1	1	yes	characteristic
6	#10587465	C₄	1	1	yes	characteristic
7	#63243	—	4	2	no	—
8	C₈×D₁₇	D₄	1	1	yes	characteristic
9	C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
10	#63214	Q₈	1	1	yes	characteristic
11	C₄×D₁₇	D₈	1	1	yes	characteristic
12	#3624	—	8	2	no	—
13	C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
14	#3622	Q₁₆	1	1	yes	characteristic
15	#1425	—	17	1	no	maximal, Sylow
16	C₂×D₁₇	Q₃₂	1	1	yes	characteristic
17	C₄×C₁₇	#107	1	1	yes	characteristic
18	Dic₁₇	D₁₆	1	1	yes	characteristic
19	C₂×C₃₂	—	17	1	no	—
20	#368	—	17	2	no	—
21	C₂×C₁₇	#366	1	1	yes	characteristic
22	D₁₇	—	2	1	no	—
23	C₂×C₁₆	—	17	1	no	—
24	#108	—	34	2	no	—
25	C₃₂	—	17	1	no	—
26	C₃₂	#595	1	1	yes	characteristic
27	C₁₇	#1425	1	1	yes	characteristic, complemented, Sylow
28	M₁₆	—	68	2	no	—
29	C₂×C₈	—	17	1	no	—
30	C₁₆	—	17	1	no	—
31	C₁₆	C₂×#595	1	1	yes	characteristic
32	C₂×C₄	—	17	1	no	—
33	C₈	—	17	1	no	—
34	C₈	—	136	2	no	—
35	C₈	C₄⋊#595	1	1	yes	characteristic
36	C₂²	—	17	1	no	—
37	C₄	—	17	1	no	—
38	C₄	#10587534	1	1	yes	characteristic
39	C₂	—	34	1	no	—
40	C₂	#11763735	1	1	yes	characteristic

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

N	H ≅ G/N	type
27. C₁₇	#1425	semidirect

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