Subgroups — #28334665

Order 13696.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20292457	C₂	1	2	yes	maximal
2	C₂×C₃₂×C₁₀₇	C₂	1	1	yes	maximal, characteristic
3	#16812045	—	2	2	no	—
4	C₂×C₁₆×C₁₀₇	C₂²	1	1	yes	characteristic
5	C₃₂×C₁₀₇	C₄	1	2	yes	—
6	#13133802	—	4	2	no	—
7	C₂×C₈×C₁₀₇	D₄	1	1	yes	characteristic
8	C₁₆×C₁₀₇	C₂×C₄	1	1	yes	characteristic
9	C₁₆×C₁₀₇	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₁₀₇	D₈	1	1	yes	characteristic
11	C₈×C₁₀₇	C₄⋊C₄	1	1	yes	characteristic
12	C₈×C₁₀₇	Q₁₆	1	1	yes	characteristic
13	C₁₀₇⋊C₈	—	8	2	no	—
14	C₂²×C₁₀₇	Q₃₂	1	1	yes	characteristic
15	C₄×C₁₀₇	#107	1	1	yes	characteristic
16	C₄×C₁₀₇	D₁₆	1	1	yes	characteristic
17	C₂×C₁₀₇	—	2	1	no	—
18	C₂×C₁₀₇	#366	1	1	yes	characteristic
19	#1425	—	107	1	no	maximal, Sylow
20	C₁₀₇	#1425	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₃₂	D₁₀₇	1	1	yes	characteristic
22	#368	—	107	2	no	—
23	C₂×C₁₆	C₂×D₁₀₇	1	1	yes	characteristic
24	#108	—	214	2	no	—
25	C₃₂	Dic₁₀₇	1	2	yes	—
26	M₁₆	—	428	2	no	—
27	C₂×C₈	D₄₂₈	1	1	yes	characteristic
28	C₁₆	Dic₂₁₄	1	1	yes	characteristic
29	C₁₆	C₂×Dic₁₀₇	1	1	yes	characteristic
30	C₂×C₄	D₈₅₆	1	1	yes	characteristic
31	C₈	—	856	2	no	—
32	C₈	C₄⋊Dic₁₀₇	1	1	yes	characteristic
33	C₈	Dic₄₂₈	1	1	yes	characteristic
34	C₂²	Dic₈₅₆	1	1	yes	characteristic
35	C₄	#16812043	1	1	yes	characteristic
36	C₄	D₁₇₁₂	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#20292453	1	1	yes	characteristic

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

N	H ≅ G/N	type
20. C₁₀₇	#1425	semidirect

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