Subgroups — #66570

Order 336.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₄₂	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₁₄	C₂	1	1	yes	maximal, characteristic
3	C₇×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	Dic₂₈	—	3	1	no	maximal, Hall
5	C₃×C₄×C₇	C₂²	1	1	yes	characteristic
6	Dic₂₁	—	2	1	no	—
7	C₃×Dic₇	—	2	1	no	—
8	Dic₁₄	—	3	1	no	—
9	Dic₁₄	D₃	1	1	yes	characteristic
10	C₇×C₈	—	3	1	no	—
11	#216	—	7	1	no	maximal, Hall
12	C₂×C₃×C₇	D₄	1	1	yes	characteristic
13	C₄×C₇	C₂×D₃	1	1	yes	characteristic
14	Dic₇	—	2	1	no	—
15	Dic₇	—	6	1	no	—
16	C₃×Q₈	—	7	1	no	—
17	Dic₆	—	7	1	no	—
18	C₃⋊C₈	D₇	1	1	yes	characteristic
19	C₃×C₇	Q₁₆	1	1	yes	characteristic, complemented, Hall
20	Q₁₆	—	21	1	no	Sylow
21	C₂×C₇	#67	1	1	yes	characteristic
22	C₃×C₄	—	14	1	no	—
23	C₃×C₄	C₂×D₇	1	1	yes	characteristic
24	Dic₃	—	14	1	no	—
25	Q₈	—	7	1	no	—
26	Q₈	—	21	1	no	—
27	C₈	—	3	1	no	—
28	C₇	#216	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃	D₂₈	1	1	yes	characteristic
30	C₄	—	14	1	no	—
31	C₄	—	42	1	no	—
32	C₄	D₃×D₇	1	1	yes	characteristic
33	C₃	Dic₂₈	1	1	yes	characteristic, complemented, Sylow
34	C₂	#4246	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.