Subgroups — C₂×Dic₂₂₃₄ #31821908

Order 17872.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₂₂₃₄	C₂	1	4	yes	maximal, direct product factor
2	C₂×Dic₁₁₁₇	C₂	1	2	yes	maximal
3	C₂×C₄×C₁₁₁₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₁₁₇	C₂²	1	1	yes	characteristic
5	C₄×C₁₁₁₇	C₂²	1	2	yes	—
6	Dic₁₁₁₇	C₂²	1	4	yes	—
7	C₂×C₁₁₁₇	Q₈	1	2	yes	complemented
8	C₂×C₁₁₁₇	C₂³	1	1	yes	characteristic
9	C₁₁₁₇	C₂×Q₈	1	1	yes	characteristic, complemented, Sylow
10	C₂×Q₈	—	1117	1	no	maximal, Sylow
11	Q₈	—	1117	4	no	—
12	C₂×C₄	—	1117	2	no	—
13	C₂×C₄	D₁₁₁₇	1	1	yes	characteristic
14	C₂²	C₂×D₁₁₁₇	1	1	yes	characteristic
15	C₄	—	1117	4	no	—
16	C₄	C₂×D₁₁₁₇	1	2	yes	—
17	C₂	Dic₂₂₃₄	1	2	yes	direct product factor
18	C₂	C₂²×D₁₁₁₇	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.