Subgroups — #20295932

Order 6976.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812758	C₂	1	2	yes	maximal
2	#16812688	C₂	1	1	yes	maximal, characteristic
3	C₂²⋊#89137	—	2	2	no	—
4	C₂×D₄₃₆	C₂²	1	1	yes	characteristic
5	#13182006	—	2	2	no	—
6	C₄×Dic₁₀₉	C₄	1	1	yes	characteristic, complemented
7	C₂×Q₈×C₁₀₉	C₄	1	1	yes	characteristic, complemented
8	C₂²×D₁₀₉	D₄	1	2	yes	—
9	C₂×#89137	—	4	2	no	—
10	Q₈×C₁₀₉	—	4	1	no	—
11	C₂×C₄×C₁₀₉	—	2	1	no	—
12	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
13	C₂×Dic₁₀₉	—	2	1	no	—
14	D₄₃₆	—	4	1	no	—
15	C₂²×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
16	C₂×D₁₀₉	—	2	2	no	—
17	C₂×D₁₀₉	—	4	2	no	—
18	#89137	—	8	2	no	—
19	C₄×C₁₀₉	—	2	1	no	—
20	C₄×C₁₀₉	—	4	1	no	—
21	Dic₁₀₉	—	4	1	no	—
22	C₂×C₁₀₉	—	2	1	no	—
23	C₂×C₁₀₉	#99	1	1	yes	characteristic
24	D₁₀₉	—	4	2	no	—
25	C₁₀₉	#354	1	1	yes	characteristic, complemented, Sylow
26	#354	—	109	1	no	maximal, Sylow
27	#124	—	109	1	no	—
28	#99	—	109	2	no	—
29	C₂×Q₈	#89137	1	1	yes	characteristic, complemented
30	C₂×D₄	—	109	1	no	—
31	C₂²⋊C₄	—	218	2	no	—
32	C₂²⋊C₄	—	218	2	no	—
33	C₄²	—	109	1	no	—
34	C₂³	—	109	2	no	—
35	Q₈	—	4	1	no	—
36	D₄	—	436	1	no	—
37	C₂×C₄	—	2	1	no	—
38	C₂×C₄	—	436	2	no	—
39	C₂×C₄	—	218	1	no	—
40	C₂×C₄	C₂×#89137	1	1	yes	characteristic
41	C₂²	—	436	2	no	—
42	C₂²	—	218	2	no	—
43	C₂²	C₂²⋊#89137	1	1	yes	characteristic
44	C₄	—	2	1	no	—
45	C₄	—	4	1	no	—
46	C₄	—	872	2	no	—
47	C₄	—	436	1	no	—
48	C₂	—	2	1	no	—
49	C₂	—	436	2	no	—
50	C₂	#16812757	1	1	yes	characteristic

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