Subgroups — #6437

Order 224.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₈	C₂	1	6	yes	maximal, complemented
2	C₄²×C₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×D₇	C₂²	1	4	yes	—
4	C₂×C₄×C₇	C₂²	1	3	yes	—
5	D₂₈	—	2	12	no	—
6	#127	—	7	1	no	maximal, Sylow
7	C₂²×C₇	C₂³	1	1	yes	characteristic
8	C₂×D₇	—	2	12	no	—
9	C₄×C₇	D₄	1	6	yes	complemented
10	C₂×D₄	—	7	6	no	—
11	C₄²	D₇	1	1	yes	characteristic, complemented
12	C₂×C₇	C₂×D₄	1	3	yes	—
13	D₇	—	4	4	no	—
14	C₂³	—	7	4	no	—
15	D₄	—	14	12	no	—
16	C₂×C₄	C₂×D₇	1	3	yes	—
17	C₇	#127	1	1	yes	characteristic, complemented, Sylow
18	C₂²	—	14	12	no	—
19	C₂²	C₂²×D₇	1	1	yes	characteristic
20	C₄	D₂₈	1	6	yes	complemented
21	C₂	—	28	4	no	—
22	C₂	C₂×D₂₈	1	3	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.