Subgroups — C₂×#16812749 #20295956

Order 6976.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812749	C₂	1	2	yes	maximal, direct product factor
2	C₂×#13182004	C₂	1	1	yes	maximal, characteristic
3	#13182004	C₄	1	1	yes	characteristic
4	#13182004	C₂²	1	1	yes	characteristic
5	C₂×C₈×C₁₀₉	C₄	1	1	yes	characteristic
6	C₂×C₄×C₁₀₉	C₈	1	1	yes	characteristic
7	C₈×C₁₀₉	C₈	1	1	yes	characteristic
8	C₈×C₁₀₉	C₂×C₄	1	1	yes	characteristic
9	C₂²×C₁₀₉	C₁₆	1	1	yes	characteristic
10	C₄×C₁₀₉	C₁₆	1	1	yes	characteristic
11	C₄×C₁₀₉	C₂×C₈	1	1	yes	characteristic
12	C₂×C₁₀₉	C₃₂	1	2	yes	complemented
13	C₂×C₁₀₉	C₂×C₁₆	1	1	yes	characteristic
14	C₁₀₉	C₂×C₃₂	1	1	yes	characteristic, complemented, Sylow
15	C₂×C₃₂	—	109	1	no	maximal, Sylow
16	C₂×C₁₆	—	109	1	no	—
17	C₃₂	—	109	2	no	—
18	C₂×C₈	#89137	1	1	yes	characteristic
19	C₁₆	—	109	1	no	—
20	C₁₆	—	109	1	no	—
21	C₂×C₄	#11724786	1	1	yes	characteristic
22	C₈	#11724786	1	1	yes	characteristic
23	C₈	C₂×#89137	1	1	yes	characteristic
24	C₂²	#13182032	1	1	yes	characteristic
25	C₄	#13182032	1	1	yes	characteristic
26	C₄	C₂×#11724786	1	1	yes	characteristic
27	C₂	#16812749	1	2	yes	direct product factor
28	C₂	C₂×#13182032	1	1	yes	characteristic

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