Subgroups — #20292449

Order 6848.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812049	C₂	1	1	yes	maximal, characteristic
2	#16812045	C₂	1	1	yes	maximal, characteristic
3	#106×C₁₀₇	C₂	1	1	yes	maximal, characteristic
4	#13133802	—	2	1	no	—
5	C₁₀₇⋊C₁₆	C₄	1	2	yes	complemented
6	C₂×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
7	C₄⋊C₄×C₁₀₇	—	2	1	no	—
8	C₂×C₄×C₁₀₇	—	4	1	no	—
9	C₂×C₄×C₁₀₇	D₄	1	1	yes	characteristic
10	C₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
11	C₈×C₁₀₇	Q₈	1	1	yes	characteristic
12	C₁₀₇⋊C₈	—	4	1	no	—
13	C₂²×C₁₀₇	SD₁₆	1	1	yes	characteristic
14	C₄×C₁₀₇	—	8	1	no	—
15	C₄×C₁₀₇	C₄⋊C₄	1	1	yes	characteristic
16	C₄×C₁₀₇	SD₁₆	1	1	yes	characteristic
17	C₂×C₁₀₇	—	2	1	no	—
18	C₂×C₁₀₇	#106	1	1	yes	characteristic
19	C₁₀₇	#365	1	1	yes	characteristic, complemented, Sylow
20	#365	—	107	1	no	maximal, Sylow
21	M₃₂	—	107	1	no	—
22	#108	—	107	1	no	—
23	#106	D₁₀₇	1	1	yes	characteristic
24	M₁₆	—	214	1	no	—
25	C₂×C₈	C₂×D₁₀₇	1	1	yes	characteristic
26	C₄⋊C₄	—	2	1	no	—
27	C₁₆	—	107	2	no	—
28	C₂×C₄	—	4	1	no	—
29	C₂×C₄	C₂²⋊D₁₀₇	1	1	yes	characteristic
30	C₈	—	428	1	no	—
31	C₈	Dic₂₁₄	1	1	yes	characteristic
32	C₈	C₄×D₁₀₇	1	1	yes	characteristic
33	C₂²	#13133806	1	1	yes	characteristic
34	C₄	—	8	1	no	—
35	C₄	Dic₁₀₇⋊C₄	1	1	yes	characteristic
36	C₄	#13133805	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#16812040	1	1	yes	characteristic

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

N	H ≅ G/N	type
5. C₁₀₇⋊C₁₆	C₄	semidirect
19. C₁₀₇	#365	semidirect