Subgroups — #20295881

Order 6976.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812754	C₂	1	2	yes	maximal, complemented
2	#16812686	C₂	1	1	yes	maximal, characteristic
3	C₂×#11724786	—	2	2	no	—
4	C₂×Dic₂₁₈	C₄	1	1	yes	characteristic
5	C₂²⋊Dic₁₀₉	—	2	2	no	—
6	C₄×Dic₁₀₉	C₂²	1	1	yes	characteristic
7	C₂×D₄×C₁₀₉	C₄	1	1	yes	characteristic
8	C₂³×C₁₀₉	—	2	1	no	—
9	D₄×C₁₀₉	—	4	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	—	2	4	no	—
15	C₂²×C₁₀₉	—	4	1	no	—
16	C₂²×C₁₀₉	—	4	2	no	—
17	C₂²×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
18	C₄×C₁₀₉	—	2	1	no	—
19	Dic₁₀₉	—	2	2	no	—
20	Dic₁₀₉	—	4	1	no	—
21	C₂×C₁₀₉	—	8	1	no	—
22	C₂×C₁₀₉	#100	1	1	yes	characteristic
23	C₂×C₁₀₉	#104	1	2	yes	—
24	C₁₀₉	#329	1	1	yes	characteristic, complemented, Sylow
25	#329	—	109	1	no	maximal, Sylow
26	#124	—	109	1	no	—
27	#97	—	109	2	no	—
28	C₂×Q₈	—	109	1	no	—
29	C₂×D₄	#89137	1	1	yes	characteristic
30	C₂×C₈	—	218	2	no	—
31	C₂²⋊C₄	—	218	2	no	—
32	C₄²	—	109	1	no	—
33	C₂³	—	2	1	no	—
34	Q₈	—	436	1	no	—
35	D₄	—	4	1	no	—
36	C₂×C₄	—	109	2	no	—
37	C₂×C₄	—	218	1	no	—
38	C₂×C₄	C₂×#89137	1	1	yes	characteristic
39	C₈	—	218	4	no	—
40	C₂²	—	4	1	no	—
41	C₂²	—	4	2	no	—
42	C₂²	C₂²⋊#89137	1	1	yes	characteristic
43	C₄	—	2	1	no	—
44	C₄	—	436	1	no	—
45	C₄	—	218	2	no	—
46	C₂	—	8	1	no	—
47	C₂	#16812759	1	1	yes	characteristic
48	C₂	#16812763	1	2	yes	—

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

N	H ≅ G/N	type
1. #16812754	C₂	semidirect
24. C₁₀₉	#329	semidirect