Subgroups — #28334677

Order 13696.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₇₁₂	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃₄₂₄	C₂	1	1	yes	maximal, characteristic
3	C₆₄×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₈₅₆	—	2	1	no	—
5	D₁₇₁₂	—	2	1	no	—
6	C₃₂×C₁₀₇	C₂²	1	1	yes	characteristic
7	Dic₄₂₈	—	4	1	no	—
8	D₈₅₆	—	4	1	no	—
9	C₁₆×C₁₀₇	D₄	1	1	yes	characteristic
10	D₄₂₈	—	8	1	no	—
11	Dic₂₁₄	—	8	1	no	—
12	C₈×C₁₀₇	D₈	1	1	yes	characteristic
13	C₂×D₁₀₇	—	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	D₁₀₇	—	32	1	no	—
18	SD₁₂₈	—	107	1	no	maximal, Sylow
19	C₁₀₇	SD₁₂₈	1	1	yes	characteristic, complemented, Sylow
20	Q₆₄	—	107	1	no	—
21	D₃₂	—	107	1	no	—
22	C₆₄	D₁₀₇	1	1	yes	characteristic, complemented
23	Q₃₂	—	214	1	no	—
24	D₁₆	—	214	1	no	—
25	C₃₂	C₂×D₁₀₇	1	1	yes	characteristic
26	Q₁₆	—	428	1	no	—
27	D₈	—	428	1	no	—
28	C₁₆	D₄₂₈	1	1	yes	characteristic
29	Q₈	—	856	1	no	—
30	D₄	—	856	1	no	—
31	C₈	D₈₅₆	1	1	yes	characteristic
32	C₂²	—	1712	1	no	—
33	C₄	—	1712	1	no	—
34	C₄	D₁₇₁₂	1	1	yes	characteristic
35	C₂	—	3424	1	no	—
36	C₂	D₃₄₂₄	1	1	yes	characteristic

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

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