Subgroups — #20296084

Order 6976.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812773	C₂	1	3	yes	maximal, complemented
2	C₂×#13182032	C₂	1	3	yes	maximal, complemented
3	#16812706	C₂	1	1	yes	maximal, characteristic
4	#13182032	C₂²	1	1	yes	characteristic
5	#13182032	C₂²	1	3	yes	—
6	#13182013	C₄	1	3	yes	—
7	C₂×#11724784	C₂²	1	3	yes	—
8	#41×C₁₀₉	C₄	1	1	yes	characteristic
9	Q₈×C₁₀₉	C₈	1	1	yes	characteristic
10	D₄×C₁₀₉	C₈	1	3	yes	—
11	C₂×C₄×C₁₀₉	C₂×C₄	1	3	yes	—
12	#11724784	C₂×C₄	1	3	yes	—
13	#11724784	C₂³	1	1	yes	characteristic
14	C₂²×C₁₀₉	C₂×C₈	1	3	yes	—
15	C₄×C₁₀₉	C₂×C₈	1	3	yes	—
16	C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
17	C₂×C₁₀₉	—	2	3	no	—
18	C₂×C₁₀₉	C₂²×C₈	1	1	yes	characteristic
19	C₁₀₉	#504	1	1	yes	characteristic, complemented, Sylow
20	#504	—	109	1	no	maximal, Sylow
21	#131	—	109	1	no	—
22	M₃₂	—	109	3	no	—
23	C₂×C₁₆	—	109	3	no	—
24	#41	#89137	1	1	yes	characteristic
25	M₁₆	—	109	3	no	—
26	C₂×C₈	—	109	3	no	—
27	C₁₆	—	109	1	no	—
28	C₁₆	—	109	3	no	—
29	Q₈	#11724786	1	1	yes	characteristic
30	D₄	#11724786	1	3	yes	—
31	C₂×C₄	C₂×#89137	1	3	yes	—
32	C₈	—	109	1	no	—
33	C₈	—	109	3	no	—
34	C₂²	C₂×#11724786	1	3	yes	—
35	C₄	C₂×#11724786	1	3	yes	—
36	C₄	C₂²×#89137	1	1	yes	characteristic
37	C₂	—	2	3	no	—
38	C₂	C₂²×#11724786	1	1	yes	characteristic

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