Subgroups — #20295949

Order 6976.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812773	C₂	1	2	yes	maximal
2	C₄×#11724784	C₂	1	1	yes	maximal, characteristic
3	#13182032	—	2	2	no	—
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	—	2	1	no	—
8	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
9	#11724784	C₈	1	2	yes	—
10	#11724784	D₄	1	1	yes	characteristic
11	#11724784	Q₈	1	1	yes	characteristic
12	C₂²×C₁₀₉	M₁₆	1	1	yes	characteristic
13	C₄×C₁₀₉	—	2	2	no	—
14	C₄×C₁₀₉	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₁₀₉	C₂×C₈	1	1	yes	characteristic
16	C₂×C₁₀₉	—	2	1	no	—
17	C₂×C₁₀₉	C₄⋊C₈	1	1	yes	characteristic
18	C₁₀₉	#364	1	1	yes	characteristic, complemented, Sylow
19	#364	—	109	1	no	maximal, Sylow
20	M₃₂	—	109	2	no	—
21	C₄×C₈	—	109	1	no	—
22	C₂×C₈	—	109	1	no	—
23	C₂×C₈	—	109	1	no	—
24	C₄²	#89137	1	1	yes	characteristic
25	C₁₆	—	218	2	no	—
26	C₂×C₄	—	2	1	no	—
27	C₂×C₄	C₂×#89137	1	1	yes	characteristic
28	C₈	—	109	1	no	—
29	C₈	—	109	1	no	—
30	C₈	—	109	2	no	—
31	C₂²	#13182038	1	1	yes	characteristic
32	C₄	—	2	2	no	—
33	C₄	C₄⋊#89137	1	1	yes	characteristic
34	C₄	D₁₀₉⋊C₈	1	1	yes	characteristic
35	C₂	—	2	1	no	—
36	C₂	#16812766	1	1	yes	characteristic

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

N	H ≅ G/N	type
18. C₁₀₉	#364	semidirect