Subgroups — #14526988

Order 2176.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11762639	C₂	1	2	yes	maximal
2	C₂×C₁₇×C₃₂	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₁₇	C₂²	1	1	yes	characteristic
4	#10587490	—	2	2	no	—
5	C₁₇×C₃₂	C₄	1	2	yes	—
6	C₂×C₈×C₁₇	D₄	1	1	yes	characteristic
7	#63223	—	4	2	no	—
8	C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
9	C₁₆×C₁₇	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₁₇	D₈	1	1	yes	characteristic
11	C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
12	C₈×C₁₇	Q₁₆	1	1	yes	characteristic
13	#3622	—	8	2	no	—
14	#1425	—	17	1	no	maximal, Sylow
15	C₂²×C₁₇	Q₃₂	1	1	yes	characteristic
16	C₄×C₁₇	#107	1	1	yes	characteristic
17	C₄×C₁₇	D₁₆	1	1	yes	characteristic
18	C₂×C₃₂	D₁₇	1	1	yes	characteristic
19	#368	—	17	2	no	—
20	C₂×C₁₇	—	2	1	no	—
21	C₂×C₁₇	#366	1	1	yes	characteristic
22	C₂×C₁₆	C₂×D₁₇	1	1	yes	characteristic
23	#108	—	34	2	no	—
24	C₃₂	Dic₁₇	1	2	yes	—
25	C₁₇	#1425	1	1	yes	characteristic, complemented, Sylow
26	M₁₆	—	68	2	no	—
27	C₂×C₈	D₆₈	1	1	yes	characteristic
28	C₁₆	Dic₃₄	1	1	yes	characteristic
29	C₁₆	C₂×Dic₁₇	1	1	yes	characteristic
30	C₂×C₄	D₁₃₆	1	1	yes	characteristic
31	C₈	—	136	2	no	—
32	C₈	Dic₆₈	1	1	yes	characteristic
33	C₈	C₄⋊Dic₁₇	1	1	yes	characteristic
34	C₂²	Dic₁₃₆	1	1	yes	characteristic
35	C₄	D₂₇₂	1	1	yes	characteristic
36	C₄	#10587489	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#11762635	1	1	yes	characteristic

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

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

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