Subgroups — #20295971

Order 6976.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₂×#89137)⋊C₄	C₂	1	6	yes	maximal
2	C₄²×D₁₀₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×#89137	C₂²	1	4	yes	—
4	C₂×C₄×D₁₀₉	C₂²	1	3	yes	—
5	C₄×Dic₁₀₉	C₄	1	3	yes	complemented
6	C₄²×C₁₀₉	C₄	1	1	yes	characteristic, complemented
7	C₂²×D₁₀₉	C₂³	1	1	yes	characteristic
8	C₂×#89137	—	2	12	no	—
9	C₂×C₄×C₁₀₉	C₂×C₄	1	3	yes	—
10	C₂×Dic₁₀₉	C₂×C₄	1	3	yes	—
11	C₄×D₁₀₉	—	2	6	no	—
12	C₂²×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
13	C₂×D₁₀₉	#41	1	6	yes	—
14	#89137	—	4	4	no	—
15	C₄×C₁₀₉	—	2	3	no	—
16	Dic₁₀₉	—	2	3	no	—
17	C₂×C₁₀₉	#117	1	3	yes	—
18	D₁₀₉	#126	1	4	yes	—
19	C₁₀₉	#383	1	1	yes	characteristic, complemented, Sylow
20	#383	—	109	1	no	maximal, Sylow
21	C₂×C₄²	—	109	1	no	—
22	#95	—	109	6	no	—
23	C₂²×C₄	—	109	3	no	—
24	C₂²×C₄	—	109	4	no	—
25	C₄²	—	109	3	no	—
26	C₄²	#89137	1	1	yes	characteristic, complemented
27	C₂³	—	109	1	no	—
28	C₂×C₄	—	109	3	no	—
29	C₂×C₄	—	218	6	no	—
30	C₂×C₄	—	218	12	no	—
31	C₂×C₄	C₂×#89137	1	3	yes	—
32	C₂²	—	109	6	no	—
33	C₂²	C₂²×#89137	1	1	yes	characteristic
34	C₄	—	2	3	no	—
35	C₄	—	436	4	no	—
36	C₄	—	218	3	no	—
37	C₂	—	109	4	no	—
38	C₂	#16812778	1	3	yes	—

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