Subgroups — #6439

Order 224.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×C₇	C₂	1	1	yes	maximal, characteristic, complemented
2	(C₂×D₇)⋊C₄	C₂	1	3	yes	maximal
3	Dic₇⋊C₄	C₂	1	3	yes	maximal, complemented
4	C₂²×D₇	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₇	C₂²	1	3	yes	—
6	C₂×Dic₇	C₂²	1	3	yes	—
7	#126	—	7	1	no	maximal, Sylow
8	C₂²×C₇	C₂³	1	1	yes	characteristic
9	C₂×D₇	—	2	3	no	—
10	C₄×C₇	—	2	3	no	—
11	Dic₇	—	2	3	no	—
12	C₄⋊C₄	—	7	3	no	—
13	C₂²⋊C₄	—	7	3	no	—
14	C₄²	D₇	1	1	yes	characteristic, complemented
15	C₂×C₇	#41	1	3	yes	—
16	D₇	—	4	1	no	—
17	C₂³	—	7	1	no	—
18	C₂×C₄	—	7	3	no	—
19	C₂×C₄	C₂×D₇	1	3	yes	—
20	C₇	#126	1	1	yes	characteristic, complemented, Sylow
21	C₂²	—	14	3	no	—
22	C₂²	C₂²×D₇	1	1	yes	characteristic
23	C₄	—	2	3	no	—
24	C₄	—	14	3	no	—
25	C₂	—	28	1	no	—
26	C₂	#1157	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.