Subgroups — C₂²×#14268661 #20299730

Order 7232.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14268661	C₂	1	6	yes	maximal, direct product factor
2	C₂²×#11744762	C₂	1	1	yes	maximal, characteristic
3	#14268661	C₂²	1	4	yes	direct product factor
4	C₂×#11744762	C₄	1	3	yes	—
5	C₂×#11744762	C₂²	1	3	yes	—
6	C₂²×#90673	C₄	1	1	yes	characteristic
7	C₂²×D₁₁₃	C₈	1	1	yes	characteristic
8	C₂×#90673	C₈	1	3	yes	—
9	C₂×#90673	C₂×C₄	1	3	yes	—
10	#11744762	C₂×C₄	1	3	yes	—
11	#11744762	C₂³	1	1	yes	characteristic
12	C₂²×C₁₁₃	C₁₆	1	1	yes	characteristic, complemented
13	C₂×D₁₁₃	C₁₆	1	3	yes	complemented
14	C₂×D₁₁₃	C₂×C₈	1	3	yes	—
15	#90673	C₂×C₈	1	3	yes	—
16	#90673	C₂²×C₄	1	1	yes	characteristic
17	C₂×C₁₁₃	C₂×C₁₆	1	3	yes	complemented
18	D₁₁₃	C₂×C₁₆	1	3	yes	complemented
19	D₁₁₃	C₂²×C₈	1	1	yes	characteristic
20	C₁₁₃	C₂²×C₁₆	1	1	yes	characteristic, complemented, Sylow
21	C₂²×C₁₆	—	113	1	no	maximal, Sylow
22	C₂²×C₈	—	113	1	no	—
23	C₂×C₁₆	—	113	6	no	—
24	C₂²×C₄	—	113	1	no	—
25	C₂×C₈	—	113	3	no	—
26	C₂×C₈	—	113	3	no	—
27	C₁₆	—	113	4	no	—
28	C₂³	—	113	1	no	—
29	C₂×C₄	—	113	3	no	—
30	C₂×C₄	—	113	3	no	—
31	C₈	—	113	1	no	—
32	C₈	—	113	3	no	—
33	C₂²	—	113	3	no	—
34	C₂²	—	113	3	no	—
35	C₂²	#14268661	1	1	yes	characteristic, direct product factor
36	C₄	—	113	1	no	—
37	C₄	—	113	3	no	—
38	C₂	—	113	1	no	—
39	C₂	—	113	3	no	—
40	C₂	C₂×#14268661	1	3	yes	direct product factor

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