Subgroups — C₂×#16813712 #20299704

Order 7232.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16813712	C₂	1	2	yes	maximal, direct product factor
2	C₂×#14268650	C₂	1	1	yes	maximal, characteristic
3	#14268650	C₄	1	1	yes	characteristic
4	#14268650	C₂²	1	1	yes	characteristic
5	C₂×#11744751	C₄	1	1	yes	characteristic
6	C₂×C₄×C₁₁₃	C₈	1	1	yes	characteristic
7	#11744751	C₈	1	1	yes	characteristic
8	#11744751	C₂×C₄	1	1	yes	characteristic
9	C₂²×C₁₁₃	C₁₆	1	1	yes	characteristic
10	C₄×C₁₁₃	C₁₆	1	1	yes	characteristic
11	C₄×C₁₁₃	C₂×C₈	1	1	yes	characteristic
12	C₂×C₁₁₃	C₃₂	1	2	yes	complemented
13	C₂×C₁₁₃	C₂×C₁₆	1	1	yes	characteristic
14	C₁₁₃	C₂×C₃₂	1	1	yes	characteristic, complemented, Sylow
15	C₂×C₃₂	—	113	1	no	maximal, Sylow
16	C₂×C₁₆	—	113	1	no	—
17	C₃₂	—	113	2	no	—
18	C₂×C₈	—	113	1	no	—
19	C₁₆	—	113	1	no	—
20	C₁₆	—	113	1	no	—
21	C₂×C₄	#11744762	1	1	yes	characteristic
22	C₈	—	113	1	no	—
23	C₈	—	113	1	no	—
24	C₂²	#14268659	1	1	yes	characteristic
25	C₄	#14268659	1	1	yes	characteristic
26	C₄	C₂×#11744762	1	1	yes	characteristic
27	C₂	#16813712	1	2	yes	direct product factor
28	C₂	C₂×#14268659	1	1	yes	characteristic

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