Subgroups — #14546017

Order 2176.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763917	C₂	1	3	yes	maximal, complemented
2	C₂×#10587528	C₂	1	3	yes	maximal, complemented
3	#11763867	C₂	1	1	yes	maximal, characteristic
4	#10587634	C₄	1	1	yes	characteristic
5	#10587538	C₄	1	3	yes	—
6	C₂×#63216	C₂²	1	3	yes	—
7	#10587528	C₂²	1	1	yes	characteristic
8	#10587528	C₂²	1	3	yes	—
9	#41×C₁₇	C₈	1	1	yes	characteristic
10	#63223	C₈	1	3	yes	—
11	C₂×#3622	C₂×C₄	1	3	yes	—
12	#63216	C₂×C₄	1	3	yes	—
13	#63216	C₂³	1	1	yes	characteristic
14	Q₈×C₁₇	C₁₆	1	1	yes	characteristic
15	D₄×C₁₇	C₁₆	1	3	yes	—
16	C₂×C₄×C₁₇	C₂×C₈	1	3	yes	—
17	#3622	C₂×C₈	1	3	yes	—
18	#3622	C₂²×C₄	1	1	yes	characteristic
19	#2258	—	17	1	no	maximal, Sylow
20	C₂²×C₁₇	C₂×C₁₆	1	3	yes	—
21	C₄×C₁₇	C₂×C₁₆	1	3	yes	—
22	C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
23	#504	—	17	1	no	—
24	M₆₄	—	17	3	no	—
25	C₂×C₃₂	—	17	3	no	—
26	C₂×C₁₇	—	2	3	no	—
27	C₂×C₁₇	C₂²×C₁₆	1	1	yes	characteristic
28	#131	—	17	1	no	—
29	M₃₂	—	17	3	no	—
30	C₂×C₁₆	—	17	3	no	—
31	C₃₂	—	17	1	no	—
32	C₃₂	—	17	3	no	—
33	C₁₇	#2258	1	1	yes	characteristic, complemented, Sylow
34	#41	#3633	1	1	yes	characteristic
35	M₁₆	—	17	3	no	—
36	C₂×C₈	—	17	3	no	—
37	C₁₆	—	17	1	no	—
38	C₁₆	—	17	3	no	—
39	Q₈	#63241	1	1	yes	characteristic
40	D₄	#63241	1	3	yes	—
41	C₂×C₄	C₂×#3633	1	3	yes	—
42	C₈	—	17	1	no	—
43	C₈	—	17	3	no	—
44	C₂²	C₂×#63241	1	3	yes	—
45	C₄	C₂×#63241	1	3	yes	—
46	C₄	C₂²×#3633	1	1	yes	characteristic
47	C₂	—	2	3	no	—
48	C₂	C₂²×#63241	1	1	yes	characteristic

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

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