Subgroups — C₂×#22552339 #30659646

Order 16672.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22552339	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₈×C₅₂₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₅₂₁	C₄	1	1	yes	characteristic
4	C₈×C₅₂₁	C₄	1	1	yes	characteristic
5	C₈×C₅₂₁	C₂²	1	1	yes	characteristic
6	C₂²×C₅₂₁	C₈	1	1	yes	characteristic
7	C₄×C₅₂₁	C₈	1	1	yes	characteristic
8	C₄×C₅₂₁	C₂×C₄	1	1	yes	characteristic
9	C₂×C₅₂₁	C₁₆	1	2	yes	complemented
10	C₂×C₅₂₁	C₂×C₈	1	1	yes	characteristic
11	C₅₂₁	C₂×C₁₆	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₁₆	—	521	1	no	maximal, Sylow
13	C₂×C₈	D₅₂₁	1	1	yes	characteristic
14	C₁₆	—	521	2	no	—
15	C₂×C₄	Dic₅₂₁	1	1	yes	characteristic
16	C₈	Dic₅₂₁	1	1	yes	characteristic
17	C₈	C₂×D₅₂₁	1	1	yes	characteristic
18	C₂²	#16861960	1	1	yes	characteristic
19	C₄	#16861960	1	1	yes	characteristic
20	C₄	C₂×Dic₅₂₁	1	1	yes	characteristic
21	C₂	#22552339	1	2	yes	direct product factor
22	C₂	C₂×#16861960	1	1	yes	characteristic

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

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.