Subgroups — #20294861

Order 6976.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₇₄₄	C₂	1	1	yes	maximal, characteristic, complemented
2	#16812605	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₆×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₈₇₂	—	2	1	no	—
5	D₈×C₁₀₉	—	2	1	no	—
6	C₁₆×C₁₀₉	C₂²	1	1	yes	characteristic
7	D₄×C₁₀₉	—	4	1	no	—
8	D₄₃₆	—	4	1	no	—
9	C₈×C₁₀₉	D₄	1	1	yes	characteristic
10	C₂²×C₁₀₉	—	8	1	no	—
11	C₂×D₁₀₉	—	8	1	no	—
12	C₄×C₁₀₉	D₈	1	1	yes	characteristic
13	C₂×C₁₀₉	—	16	1	no	—
14	C₂×C₁₀₉	D₁₆	1	1	yes	characteristic
15	D₁₀₉	—	16	1	no	—
16	C₁₀₉	D₃₂	1	1	yes	characteristic, complemented, Sylow
17	D₃₂	—	109	1	no	maximal, Sylow
18	D₁₆	—	109	1	no	—
19	D₁₆	D₁₀₉	1	1	yes	characteristic, complemented
20	C₃₂	—	109	1	no	—
21	D₈	—	2	1	no	—
22	D₈	—	218	1	no	—
23	C₁₆	C₂×D₁₀₉	1	1	yes	characteristic
24	D₄	—	4	1	no	—
25	D₄	—	436	1	no	—
26	C₈	C₂²⋊D₁₀₉	1	1	yes	characteristic
27	C₂²	—	8	1	no	—
28	C₂²	—	872	1	no	—
29	C₄	#13182014	1	1	yes	characteristic
30	C₂	—	16	1	no	—
31	C₂	—	1744	1	no	—
32	C₂	#16812640	1	1	yes	characteristic

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