Subgroups — C₇×#106 #6423

Order 224.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₈	C₂	1	1	yes	maximal, characteristic
2	C₇×C₄⋊C₄	C₂	1	2	yes	maximal
3	C₂×C₄×C₇	—	2	2	no	—
4	C₂×C₄×C₇	C₂²	1	1	yes	characteristic
5	C₇×C₈	C₄	1	2	yes	complemented
6	#106	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂²×C₇	D₄	1	1	yes	characteristic
8	C₄×C₇	—	4	2	no	—
9	C₄×C₇	C₂×C₄	1	1	yes	characteristic
10	C₄×C₇	Q₈	1	1	yes	characteristic
11	C₂×C₈	C₂×C₇	1	1	yes	characteristic
12	C₄⋊C₄	C₂×C₇	1	2	yes	—
13	C₂×C₇	C₄⋊C₄	1	1	yes	characteristic
14	C₂×C₇	SD₁₆	1	2	yes	—
15	C₂×C₄	—	2	2	no	—
16	C₂×C₄	C₂²×C₇	1	1	yes	characteristic
17	C₈	C₄×C₇	1	2	yes	complemented
18	C₇	#106	1	1	yes	characteristic, direct product factor, Sylow
19	C₂²	C₇×D₄	1	1	yes	characteristic
20	C₄	—	4	2	no	—
21	C₄	C₂×C₄×C₇	1	1	yes	characteristic
22	C₄	C₇×Q₈	1	1	yes	characteristic
23	C₂	C₇×C₄⋊C₄	1	1	yes	characteristic
24	C₂	C₇×SD₁₆	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.