Subgroups — #20295959

Order 6976.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812749	C₂	1	2	yes	maximal, complemented
2	C₁₆×D₁₀₉	C₂	1	1	yes	maximal, characteristic
3	C₈×D₁₀₉	C₄	1	1	yes	characteristic
4	#13182004	C₂²	1	1	yes	characteristic
5	C₁₆×C₁₀₉	C₄	1	1	yes	characteristic
6	C₄×D₁₀₉	C₈	1	1	yes	characteristic
7	C₈×C₁₀₉	C₂×C₄	1	1	yes	characteristic
8	#11724784	C₈	1	1	yes	characteristic
9	C₂×D₁₀₉	C₁₆	1	1	yes	characteristic
10	C₄×C₁₀₉	C₂×C₈	1	1	yes	characteristic
11	Dic₁₀₉	C₁₆	1	1	yes	characteristic
12	C₂×C₁₀₉	C₂×C₁₆	1	1	yes	characteristic
13	D₁₀₉	—	2	1	no	—
14	C₁₀₉	M₆₄	1	1	yes	characteristic, complemented, Sylow
15	M₆₄	—	109	1	no	maximal, Sylow
16	C₂×C₁₆	—	109	1	no	—
17	C₃₂	—	109	2	no	—
18	C₂×C₈	—	109	1	no	—
19	C₁₆	—	109	1	no	—
20	C₁₆	#89137	1	1	yes	characteristic
21	C₂×C₄	—	109	1	no	—
22	C₈	—	109	1	no	—
23	C₈	C₂×#89137	1	1	yes	characteristic
24	C₂²	—	109	1	no	—
25	C₄	—	109	1	no	—
26	C₄	D₁₀₉⋊C₈	1	1	yes	characteristic
27	C₂	—	218	1	no	—
28	C₂	D₁₀₉⋊C₁₆	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #16812749	C₂	semidirect
14. C₁₀₉	M₆₄	semidirect