Subgroups — #20295914

Order 6976.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13182032	C₂	1	2	yes	maximal
2	C₄×#11724784	C₂	1	1	yes	maximal, characteristic
3	#13182032	C₄	1	4	yes	complemented
4	C₂×#11724784	C₄	1	1	yes	characteristic
5	C₂×#11724784	C₂²	1	1	yes	characteristic
6	C₄²×C₁₀₉	C₄	1	1	yes	characteristic
7	C₂×C₄×C₁₀₉	C₈	1	2	yes	—
8	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
9	#11724784	C₈	1	2	yes	—
10	#11724784	C₂×C₄	1	2	yes	—
11	C₂²×C₁₀₉	C₂×C₈	1	1	yes	characteristic
12	C₄×C₁₀₉	—	2	2	no	—
13	C₄×C₁₀₉	C₄²	1	1	yes	characteristic
14	C₄×C₁₀₉	C₂×C₈	1	1	yes	characteristic
15	C₂×C₁₀₉	C₄×C₈	1	1	yes	characteristic
16	C₂×C₁₀₉	M₃₂	1	2	yes	—
17	C₁₀₉	#346	1	1	yes	characteristic, complemented, Sylow
18	#346	—	109	1	no	maximal, Sylow
19	C₂×C₁₆	—	109	2	no	—
20	C₄×C₈	—	109	1	no	—
21	C₂×C₈	—	109	1	no	—
22	C₂×C₈	—	109	1	no	—
23	C₄²	#89137	1	1	yes	characteristic
24	C₁₆	—	109	4	no	—
25	C₂×C₄	#11724786	1	2	yes	—
26	C₂×C₄	C₂×#89137	1	1	yes	characteristic
27	C₈	—	109	2	no	—
28	C₈	—	109	2	no	—
29	C₂²	C₂×#11724786	1	1	yes	characteristic
30	C₄	—	2	2	no	—
31	C₄	C₄×#89137	1	1	yes	characteristic
32	C₄	D₁₀₉⋊C₈	1	1	yes	characteristic
33	C₂	C₄×#11724786	1	1	yes	characteristic
34	C₂	#16812773	1	2	yes	—

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

N	H ≅ G/N	type
3. #13182032	C₄	semidirect
17. C₁₀₉	#346	semidirect