Subgroups — #28361249

Order 13952.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₇₄₄	C₂	1	1	yes	maximal, characteristic
2	#20294745	C₂	1	1	yes	maximal, characteristic
3	Q₆₄×C₁₀₉	C₂	1	1	yes	maximal, characteristic
4	Dic₈₇₂	—	2	1	no	—
5	Q₃₂×C₁₀₉	—	2	1	no	—
6	C₃₂×C₁₀₉	C₂²	1	1	yes	characteristic
7	Dic₄₃₆	—	4	1	no	—
8	Q₁₆×C₁₀₉	—	4	1	no	—
9	C₁₆×C₁₀₉	D₄	1	1	yes	characteristic
10	Q₈×C₁₀₉	—	8	1	no	—
11	Dic₂₁₈	—	8	1	no	—
12	C₈×C₁₀₉	D₈	1	1	yes	characteristic
13	C₄×C₁₀₉	—	16	1	no	—
14	C₄×C₁₀₉	D₁₆	1	1	yes	characteristic
15	Dic₁₀₉	—	16	1	no	—
16	C₂×C₁₀₉	D₃₂	1	1	yes	characteristic
17	Q₁₂₈	—	109	1	no	maximal, Sylow
18	C₁₀₉	Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
19	Q₆₄	—	109	1	no	—
20	Q₆₄	D₁₀₉	1	1	yes	characteristic
21	C₆₄	—	109	1	no	—
22	Q₃₂	—	2	1	no	—
23	Q₃₂	—	218	1	no	—
24	C₃₂	C₂×D₁₀₉	1	1	yes	characteristic
25	Q₁₆	—	4	1	no	—
26	Q₁₆	—	436	1	no	—
27	C₁₆	C₂²⋊D₁₀₉	1	1	yes	characteristic
28	Q₈	—	8	1	no	—
29	Q₈	—	872	1	no	—
30	C₈	#13182014	1	1	yes	characteristic
31	C₄	—	16	1	no	—
32	C₄	—	1744	1	no	—
33	C₄	#16812640	1	1	yes	characteristic
34	C₂	#20294861	1	1	yes	characteristic

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

N	H ≅ G/N	type
18. C₁₀₉	Q₁₂₈	semidirect

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