Subgroups — C₂×#16836606 #21418629

Order 7456.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16836606	C₂	1	2	yes	maximal, direct product factor
2	C₂×#14272345	C₂	1	1	yes	maximal, characteristic
3	#14272345	C₄	1	1	yes	characteristic
4	#14272345	C₂²	1	1	yes	characteristic
5	C₂×Dic₂₃₃	C₄	1	1	yes	characteristic
6	C₂²×C₂₃₃	C₈	1	1	yes	characteristic
7	Dic₂₃₃	C₈	1	1	yes	characteristic
8	Dic₂₃₃	C₂×C₄	1	1	yes	characteristic
9	C₂×C₂₃₃	C₁₆	1	2	yes	complemented
10	C₂×C₂₃₃	C₂×C₈	1	1	yes	characteristic
11	C₂₃₃	C₂×C₁₆	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₁₆	—	233	1	no	maximal, Sylow
13	C₂×C₈	—	233	1	no	—
14	C₁₆	—	233	2	no	—
15	C₂×C₄	—	233	1	no	—
16	C₈	—	233	1	no	—
17	C₈	—	233	1	no	—
18	C₂²	#14272347	1	1	yes	characteristic
19	C₄	—	233	1	no	—
20	C₄	—	233	1	no	—
21	C₂	#16836606	1	2	yes	direct product factor
22	C₂	C₂×#14272347	1	1	yes	characteristic

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