Subgroups — C₇×#97 #6414

Order 224.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₈	C₂	1	2	yes	maximal
2	C₄²×C₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₇	C₄	1	2	yes	—
4	C₂×C₄×C₇	C₂²	1	1	yes	characteristic
5	C₇×C₈	C₄	1	4	yes	complemented
6	#97	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂²×C₇	C₂×C₄	1	1	yes	characteristic
8	C₄×C₇	—	2	2	no	—
9	C₄×C₇	C₂×C₄	1	2	yes	—
10	C₂×C₈	C₂×C₇	1	2	yes	—
11	C₄²	C₂×C₇	1	1	yes	characteristic
12	C₂×C₇	C₄²	1	1	yes	characteristic
13	C₂×C₇	M₁₆	1	2	yes	—
14	C₂×C₄	C₄×C₇	1	2	yes	—
15	C₂×C₄	C₂²×C₇	1	1	yes	characteristic
16	C₈	C₄×C₇	1	4	yes	complemented
17	C₇	#97	1	1	yes	characteristic, direct product factor, Sylow
18	C₂²	C₂×C₄×C₇	1	1	yes	characteristic
19	C₄	—	2	2	no	—
20	C₄	C₂×C₄×C₇	1	2	yes	—
21	C₂	C₄²×C₇	1	1	yes	characteristic
22	C₂	C₇×M₁₆	1	2	yes	—

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.