Subgroups — #28334678

Order 13696.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₇₁₂	C₂	1	1	yes	maximal, characteristic
2	C₁₀₇⋊C₆₄	C₂	1	1	yes	maximal, characteristic
3	Q₆₄×C₁₀₇	C₂	1	1	yes	maximal, characteristic
4	Dic₈₅₆	—	2	1	no	—
5	Q₃₂×C₁₀₇	—	2	1	no	—
6	C₃₂×C₁₀₇	C₂²	1	1	yes	characteristic
7	Dic₄₂₈	—	4	1	no	—
8	Q₁₆×C₁₀₇	—	4	1	no	—
9	C₁₆×C₁₀₇	D₄	1	1	yes	characteristic
10	Q₈×C₁₀₇	—	8	1	no	—
11	Dic₂₁₄	—	8	1	no	—
12	C₈×C₁₀₇	D₈	1	1	yes	characteristic
13	C₄×C₁₀₇	—	16	1	no	—
14	C₄×C₁₀₇	D₁₆	1	1	yes	characteristic
15	Dic₁₀₇	—	16	1	no	—
16	C₂×C₁₀₇	D₃₂	1	1	yes	characteristic
17	Q₁₂₈	—	107	1	no	maximal, Sylow
18	C₁₀₇	Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
19	Q₆₄	—	107	1	no	—
20	Q₆₄	D₁₀₇	1	1	yes	characteristic
21	C₆₄	—	107	1	no	—
22	Q₃₂	—	2	1	no	—
23	Q₃₂	—	214	1	no	—
24	C₃₂	C₂×D₁₀₇	1	1	yes	characteristic
25	Q₁₆	—	4	1	no	—
26	Q₁₆	—	428	1	no	—
27	C₁₆	C₂²⋊D₁₀₇	1	1	yes	characteristic
28	Q₈	—	8	1	no	—
29	Q₈	—	856	1	no	—
30	C₈	#13133803	1	1	yes	characteristic
31	C₄	—	16	1	no	—
32	C₄	—	1712	1	no	—
33	C₄	#16812050	1	1	yes	characteristic
34	C₂	#20292462	1	1	yes	characteristic

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

N	H ≅ G/N	type
18. C₁₀₇	Q₁₂₈	semidirect

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