Subgroups — C₂³×Dic₇ #6555

Order 224.

236 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₇	C₂	1	14	yes	maximal, direct product factor
3	C₂³×C₇	C₄	1	8	yes	complemented
4	C₂³×C₇	C₂²	1	7	yes	—
5	C₂×Dic₇	C₂²	1	28	yes	direct product factor
6	C₂³×C₄	—	7	1	no	maximal, Sylow
7	C₂²×C₇	C₂×C₄	1	28	yes	complemented
8	C₂²×C₇	C₂³	1	7	yes	—
9	Dic₇	C₂³	1	8	yes	direct product factor
10	C₂⁴	D₇	1	1	yes	characteristic
11	C₂²×C₄	—	7	14	no	—
12	C₂×C₇	C₂²×C₄	1	14	yes	complemented
13	C₂×C₇	C₂⁴	1	1	yes	characteristic
14	C₂³	Dic₇	1	8	yes	direct product factor
15	C₂³	C₂×D₇	1	7	yes	—
16	C₂×C₄	—	7	28	no	—
17	C₇	C₂³×C₄	1	1	yes	characteristic, complemented, Sylow
18	C₂²	C₂×Dic₇	1	28	yes	direct product factor
19	C₂²	C₂²×D₇	1	7	yes	—
20	C₄	—	7	8	no	—
21	C₂	C₂²×Dic₇	1	14	yes	direct product factor
22	C₂	C₂³×D₇	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.