Subgroups — #6389

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	1	yes	maximal, characteristic
2	C₄×Dic₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₇⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₇	C₂²	1	1	yes	characteristic
5	C₂×Dic₇	C₄	1	2	yes	—
6	C₇×C₈	C₄	1	2	yes	complemented
7	C₇⋊C₈	C₄	1	2	yes	complemented
8	#97	—	7	1	no	maximal, Sylow
9	C₂²×C₇	C₂×C₄	1	1	yes	characteristic
10	C₄×C₇	C₂×C₄	1	1	yes	characteristic
11	C₄×C₇	C₂×C₄	1	1	yes	characteristic
12	Dic₇	—	2	2	no	—
13	C₂×C₈	—	7	1	no	—
14	C₂×C₈	D₇	1	1	yes	characteristic
15	C₄²	—	7	1	no	—
16	C₂×C₇	C₄²	1	1	yes	characteristic
17	C₂×C₇	M₁₆	1	2	yes	—
18	C₂×C₄	—	7	2	no	—
19	C₂×C₄	C₂×D₇	1	1	yes	characteristic
20	C₈	—	7	2	no	—
21	C₈	Dic₇	1	2	yes	complemented
22	C₇	#97	1	1	yes	characteristic, complemented, Sylow
23	C₂²	C₄×D₇	1	1	yes	characteristic
24	C₄	—	14	2	no	—
25	C₄	C₄×D₇	1	1	yes	characteristic
26	C₄	C₂×Dic₇	1	1	yes	characteristic
27	C₂	#1131	1	2	yes	—
28	C₂	C₄×Dic₇	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.