Subgroups — C₄⋊(C₇⋊C₈) #6378

Order 224.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×C₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇⋊C₈	C₂	1	2	yes	maximal
3	C₂×C₄×C₇	C₄	1	1	yes	characteristic
4	C₂×C₄×C₇	C₄	1	1	yes	characteristic
5	C₂×C₄×C₇	C₂²	1	1	yes	characteristic
6	C₇⋊C₈	—	2	2	no	—
7	C₄⋊C₈	—	7	1	no	maximal, Sylow
8	C₂²×C₇	C₂×C₄	1	1	yes	characteristic
9	C₄×C₇	—	2	1	no	—
10	C₄×C₇	C₈	1	2	yes	complemented
11	C₄×C₇	D₄	1	1	yes	characteristic
12	C₄×C₇	Q₈	1	1	yes	characteristic
13	C₂×C₈	—	7	2	no	—
14	C₄²	D₇	1	1	yes	characteristic
15	C₂×C₇	C₄⋊C₄	1	1	yes	characteristic
16	C₂×C₇	C₂×C₈	1	1	yes	characteristic
17	C₂×C₇	M₁₆	1	1	yes	characteristic
18	C₂×C₄	Dic₇	1	1	yes	characteristic
19	C₂×C₄	Dic₇	1	1	yes	characteristic
20	C₂×C₄	C₂×D₇	1	1	yes	characteristic
21	C₈	—	14	2	no	—
22	C₇	C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
23	C₂²	C₂×Dic₇	1	1	yes	characteristic
24	C₄	—	2	1	no	—
25	C₄	C₇⋊C₈	1	2	yes	complemented
26	C₄	Dic₁₄	1	1	yes	characteristic
27	C₄	D₂₈	1	1	yes	characteristic
28	C₂	C₂×C₇⋊C₈	1	1	yes	characteristic
29	C₂	#1136	1	1	yes	characteristic
30	C₂	C₄⋊Dic₇	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.