Subgroups — #20295950

Order 6976.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812769	C₂	1	1	yes	maximal, characteristic
2	#16812767	C₂	1	1	yes	maximal, characteristic
3	#16812638	C₂	1	1	yes	maximal, characteristic
4	#13182039	—	2	1	no	—
5	C₄⋊#89137	—	2	1	no	—
6	C₈×D₁₀₉	C₂²	1	1	yes	characteristic
7	#13182004	C₄	1	1	yes	characteristic, complemented
8	C₁₆×C₁₀₉	C₄	1	1	yes	characteristic, complemented
9	C₂×#89137	—	4	1	no	—
10	C₄×D₁₀₉	D₄	1	1	yes	characteristic
11	#11724786	—	4	1	no	—
12	C₈×C₁₀₉	C₂×C₄	1	1	yes	characteristic
13	#11724784	Q₈	1	1	yes	characteristic
14	C₂×D₁₀₉	SD₁₆	1	1	yes	characteristic
15	#89137	—	8	1	no	—
16	C₄×C₁₀₉	C₄⋊C₄	1	1	yes	characteristic
17	Dic₁₀₉	SD₁₆	1	1	yes	characteristic
18	C₂×C₁₀₉	#106	1	1	yes	characteristic
19	D₁₀₉	—	2	1	no	—
20	C₁₀₉	#365	1	1	yes	characteristic, complemented, Sylow
21	#365	—	109	1	no	maximal, Sylow
22	M₃₂	—	109	1	no	—
23	#108	—	109	1	no	—
24	#106	—	109	1	no	—
25	M₁₆	—	218	1	no	—
26	C₂×C₈	—	109	1	no	—
27	C₄⋊C₄	—	218	1	no	—
28	C₁₆	—	109	1	no	—
29	C₁₆	#89137	1	1	yes	characteristic, complemented
30	C₂×C₄	—	109	1	no	—
31	C₂×C₄	—	436	1	no	—
32	C₈	—	109	1	no	—
33	C₈	—	436	1	no	—
34	C₈	C₂×#89137	1	1	yes	characteristic
35	C₂²	—	109	1	no	—
36	C₄	—	872	1	no	—
37	C₄	—	109	1	no	—
38	C₄	C₄⋊#89137	1	1	yes	characteristic
39	C₂	—	218	1	no	—
40	C₂	#16812767	1	1	yes	characteristic

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