Subgroups — #20295886

Order 6976.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812766	C₂	1	2	yes	maximal
2	#16812697	C₂	1	1	yes	maximal, characteristic
3	C₂×#11724786	—	2	2	no	—
4	C₂×Dic₂₁₈	C₄	1	1	yes	characteristic
5	#13182008	—	2	2	no	—
6	C₄×Dic₁₀₉	C₂²	1	1	yes	characteristic
7	C₂×Q₈×C₁₀₉	C₄	1	1	yes	characteristic
8	Q₈×C₁₀₉	—	4	1	no	—
9	C₂×C₄×C₁₀₉	—	2	1	no	—
10	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
11	C₂×Dic₁₀₉	—	2	1	no	—
12	C₂×Dic₁₀₉	D₄	1	2	yes	—
13	Dic₂₁₈	—	4	1	no	—
14	#11724786	—	4	2	no	—
15	C₂²×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
16	C₄×C₁₀₉	—	2	1	no	—
17	C₄×C₁₀₉	—	4	1	no	—
18	Dic₁₀₉	—	4	1	no	—
19	Dic₁₀₉	SD₁₆	1	2	yes	—
20	Dic₁₀₉	Q₁₆	1	2	yes	—
21	C₂×C₁₀₉	#100	1	1	yes	characteristic
22	C₂×C₁₀₉	#103	1	2	yes	—
23	C₁₀₉	#333	1	1	yes	characteristic, complemented, Sylow
24	#333	—	109	1	no	maximal, Sylow
25	C₄⋊Q₈	—	109	1	no	—
26	C₄⋊C₈	—	109	2	no	—
27	C₂×Q₈	—	109	1	no	—
28	C₂×Q₈	#89137	1	1	yes	characteristic
29	C₂×C₈	—	218	2	no	—
30	C₄⋊C₄	—	218	2	no	—
31	C₄²	—	109	1	no	—
32	Q₈	—	4	1	no	—
33	Q₈	—	436	1	no	—
34	C₂×C₄	—	2	1	no	—
35	C₂×C₄	—	109	2	no	—
36	C₂×C₄	—	218	1	no	—
37	C₂×C₄	C₂×#89137	1	1	yes	characteristic
38	C₈	—	436	2	no	—
39	C₂²	C₂²⋊#89137	1	1	yes	characteristic
40	C₄	—	2	1	no	—
41	C₄	—	4	1	no	—
42	C₄	—	109	2	no	—
43	C₄	—	109	2	no	—
44	C₄	—	436	1	no	—
45	C₂	#16812759	1	1	yes	characteristic
46	C₂	#16812762	1	2	yes	—

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

N	H ≅ G/N	type
23. C₁₀₉	#333	semidirect