Subgroups — #20292405

Order 6848.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812049	C₂	1	2	yes	maximal
2	#97×C₁₀₇	C₂	1	1	yes	maximal, characteristic
3	C₁₀₇⋊C₁₆	C₄	1	4	yes	complemented
4	C₂×C₈×C₁₀₇	C₄	1	1	yes	characteristic
5	C₂×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
6	C₄²×C₁₀₇	C₄	1	1	yes	characteristic
7	C₂×C₄×C₁₀₇	—	2	1	no	—
8	C₂×C₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic
9	C₈×C₁₀₇	—	2	1	no	—
10	C₈×C₁₀₇	C₂×C₄	1	2	yes	—
11	C₂²×C₁₀₇	M₁₆	1	1	yes	characteristic
12	C₄×C₁₀₇	—	4	1	no	—
13	C₄×C₁₀₇	C₄²	1	1	yes	characteristic
14	C₄×C₁₀₇	M₁₆	1	1	yes	characteristic
15	C₂×C₁₀₇	—	2	1	no	—
16	C₂×C₁₀₇	#97	1	1	yes	characteristic
17	C₁₀₇	#347	1	1	yes	characteristic, complemented, Sylow
18	#347	—	107	1	no	maximal, Sylow
19	M₃₂	—	107	2	no	—
20	#97	D₁₀₇	1	1	yes	characteristic
21	C₂×C₈	Dic₁₀₇	1	1	yes	characteristic
22	C₂×C₈	C₂×D₁₀₇	1	1	yes	characteristic
23	C₄²	Dic₁₀₇	1	1	yes	characteristic
24	C₁₆	—	107	4	no	—
25	C₂×C₄	—	2	1	no	—
26	C₂×C₄	C₂×Dic₁₀₇	1	1	yes	characteristic
27	C₈	—	2	1	no	—
28	C₈	C₄×D₁₀₇	1	2	yes	—
29	C₂²	#13133802	1	1	yes	characteristic
30	C₄	—	4	1	no	—
31	C₄	C₄×Dic₁₀₇	1	1	yes	characteristic
32	C₄	#13133802	1	1	yes	characteristic
33	C₂	—	2	1	no	—
34	C₂	#16812020	1	1	yes	characteristic

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

N	H ≅ G/N	type
3. C₁₀₇⋊C₁₆	C₄	semidirect
17. C₁₀₇	#347	semidirect