Subgroups — #14545846

Order 2176.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763913	C₂	1	2	yes	maximal
2	#11763696	C₂	1	1	yes	maximal, characteristic
3	#10587666	—	2	2	no	—
4	C₈×#595	C₂²	1	1	yes	characteristic
5	#10587529	C₄	1	1	yes	characteristic
6	C₁₆×D₁₇	C₄	1	1	yes	characteristic
7	C₄×#595	Q₈	1	1	yes	characteristic
8	#63242	D₄	1	1	yes	characteristic
9	#63241	—	4	2	no	—
10	C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
11	#63216	—	2	1	no	—
12	C₁₆×C₁₇	C₈	1	1	yes	characteristic
13	#63214	C₈	1	1	yes	characteristic
14	C₂×#595	—	2	1	no	—
15	C₄×D₁₇	C₄⋊C₄	1	1	yes	characteristic
16	#3624	SD₁₆	1	2	yes	—
17	C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
18	#3622	M₁₆	1	1	yes	characteristic
19	#1369	—	17	1	no	maximal, Sylow
20	C₂×D₁₇	#108	1	1	yes	characteristic
21	#595	—	4	1	no	—
22	C₄×C₁₇	C₄⋊C₈	1	1	yes	characteristic
23	Dic₁₇	#106	1	1	yes	characteristic
24	#364	—	17	2	no	—
25	#346	—	17	1	no	—
26	C₂×C₁₇	#334	1	1	yes	characteristic
27	D₁₇	—	2	1	no	—
28	M₃₂	—	34	2	no	—
29	C₂×C₁₆	—	17	1	no	—
30	C₂×C₁₆	—	17	1	no	—
31	C₄×C₈	—	17	1	no	—
32	C₁₇	#1369	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₈	—	17	1	no	—
34	C₂×C₈	—	17	1	no	—
35	C₄²	—	17	1	no	—
36	C₁₆	—	17	1	no	—
37	C₁₆	—	34	1	no	—
38	C₁₆	—	68	2	no	—
39	C₁₆	#3633	1	1	yes	characteristic
40	C₂×C₄	—	17	1	no	—
41	C₂×C₄	—	34	1	no	—
42	C₈	—	17	2	no	—
43	C₈	—	17	1	no	—
44	C₈	C₂×#3633	1	1	yes	characteristic
45	C₂²	—	17	1	no	—
46	C₄	—	17	1	no	—
47	C₄	—	68	1	no	—
48	C₄	C₄⋊#3633	1	1	yes	characteristic
49	C₂	—	34	1	no	—
50	C₂	#11763898	1	1	yes	characteristic

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

N	H ≅ G/N	type
32. C₁₇	#1369	semidirect

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