Subgroups — C₂²×C₇×C₈ #6532

Order 224.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×C₈	C₂	1	6	yes	maximal, direct product factor
3	C₂³×C₇	C₄	1	1	yes	characteristic
4	C₂×C₄×C₇	C₄	1	3	yes	—
5	C₂×C₄×C₇	C₂²	1	3	yes	—
6	C₇×C₈	C₂²	1	4	yes	direct product factor
7	C₂²×C₈	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
8	C₂²×C₇	C₈	1	4	yes	direct product factor
9	C₂²×C₇	C₂×C₄	1	3	yes	—
10	C₄×C₇	C₂×C₄	1	3	yes	—
11	C₄×C₇	C₂³	1	1	yes	characteristic
12	C₂²×C₄	C₂×C₇	1	1	yes	characteristic
13	C₂×C₈	C₂×C₇	1	6	yes	direct product factor
14	C₂×C₇	C₂×C₈	1	6	yes	direct product factor
15	C₂×C₇	C₂²×C₄	1	1	yes	characteristic
16	C₂³	C₄×C₇	1	1	yes	characteristic
17	C₂×C₄	C₄×C₇	1	3	yes	—
18	C₂×C₄	C₂²×C₇	1	3	yes	—
19	C₈	C₂²×C₇	1	4	yes	direct product factor
20	C₇	C₂²×C₈	1	1	yes	characteristic, direct product factor, Sylow
21	C₂²	C₇×C₈	1	4	yes	direct product factor
22	C₂²	C₂×C₄×C₇	1	3	yes	—
23	C₄	C₂×C₄×C₇	1	3	yes	—
24	C₄	C₂³×C₇	1	1	yes	characteristic
25	C₂	C₂×C₇×C₈	1	6	yes	direct product factor
26	C₂	C₂²×C₄×C₇	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.