Subgroups — C₂×Dic₁₃₆₆ #24926419

Order 10928.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₃₆₆	C₂	1	4	yes	maximal, direct product factor
2	C₂×Dic₆₈₃	C₂	1	2	yes	maximal
3	C₂×C₄×C₆₈₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₆₈₃	C₂²	1	1	yes	characteristic
5	C₄×C₆₈₃	C₂²	1	2	yes	—
6	Dic₆₈₃	C₂²	1	4	yes	—
7	C₂×C₆₈₃	Q₈	1	2	yes	complemented
8	C₂×C₆₈₃	C₂³	1	1	yes	characteristic
9	C₆₈₃	C₂×Q₈	1	1	yes	characteristic, complemented, Sylow
10	C₂×Q₈	—	683	1	no	maximal, Sylow
11	Q₈	—	683	4	no	—
12	C₂×C₄	—	683	2	no	—
13	C₂×C₄	D₆₈₃	1	1	yes	characteristic
14	C₂²	C₂×D₆₈₃	1	1	yes	characteristic
15	C₄	—	683	4	no	—
16	C₄	C₂×D₆₈₃	1	2	yes	—
17	C₂	Dic₁₃₆₆	1	2	yes	direct product factor
18	C₂	C₂²×D₆₈₃	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.