Subgroups — C₂×C₁₃₆₇⋊C₈ #36346166

Order 21872.

22 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃₆₇⋊C₈	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₄×C₁₃₆₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₃₆₇	C₄	1	1	yes	characteristic
4	C₄×C₁₃₆₇	C₄	1	1	yes	characteristic
5	C₄×C₁₃₆₇	C₂²	1	1	yes	characteristic
6	C₂×C₁₃₆₇	C₈	1	2	yes	complemented
7	C₂×C₁₃₆₇	C₂×C₄	1	1	yes	characteristic
8	C₁₃₆₇	C₂×C₈	1	1	yes	characteristic, complemented, Sylow
9	C₂×C₈	—	1367	1	no	maximal, Sylow
10	C₂×C₄	D₁₃₆₇	1	1	yes	characteristic
11	C₈	—	1367	2	no	—
12	C₂²	Dic₁₃₆₇	1	1	yes	characteristic
13	C₄	Dic₁₃₆₇	1	1	yes	characteristic
14	C₄	C₂×D₁₃₆₇	1	1	yes	characteristic
15	C₂	C₁₃₆₇⋊C₈	1	2	yes	direct product factor
16	C₂	C₂×Dic₁₃₆₇	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.