Subgroups — C₃×Dic₂₈ #66593

Order 336.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Dic₁₄	C₂	1	2	yes	maximal
2	C₃×C₇×C₈	C₂	1	1	yes	maximal, characteristic
3	Dic₂₈	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₄×C₇	C₂²	1	1	yes	characteristic
5	C₃×Dic₇	—	2	2	no	—
6	Dic₁₄	C₂×C₃	1	2	yes	—
7	C₇×C₈	C₂×C₃	1	1	yes	characteristic
8	C₃×Q₁₆	—	7	1	no	maximal, Hall
9	C₂×C₃×C₇	D₄	1	1	yes	characteristic
10	C₄×C₇	C₂²×C₃	1	1	yes	characteristic
11	Dic₇	—	2	2	no	—
12	C₃×Q₈	—	7	2	no	—
13	C₃×C₈	D₇	1	1	yes	characteristic
14	C₃×C₇	Q₁₆	1	1	yes	characteristic, complemented, Hall
15	Q₁₆	—	7	1	no	Sylow
16	C₂×C₇	C₃×D₄	1	1	yes	characteristic
17	C₃×C₄	—	14	2	no	—
18	C₃×C₄	C₂×D₇	1	1	yes	characteristic
19	Q₈	—	7	2	no	—
20	C₈	C₃×D₇	1	1	yes	characteristic
21	C₇	C₃×Q₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₃	D₂₈	1	1	yes	characteristic
23	C₄	—	14	2	no	—
24	C₄	C₂×C₃×D₇	1	1	yes	characteristic
25	C₃	Dic₂₈	1	1	yes	characteristic, direct product factor, Sylow
26	C₂	C₃×D₂₈	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.