Subgroups — C₄×C₇×Dic₃ #66612

Order 336.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×Dic₃	C₂	1	2	yes	maximal
3	C₄²×C₇	—	3	1	no	maximal, Hall
4	C₂²×C₃×C₇	C₂²	1	1	yes	characteristic
5	C₃×C₄×C₇	C₄	1	2	yes	complemented
6	C₇×Dic₃	C₄	1	4	yes	direct product factor
7	C₂×C₄×C₇	—	3	2	no	—
8	C₂×C₄×C₇	D₃	1	1	yes	characteristic
9	C₄×Dic₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×C₇	C₂×C₄	1	2	yes	—
11	C₂×C₃×C₇	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₇	C₂×D₃	1	1	yes	characteristic
13	C₄×C₇	—	3	4	no	—
14	C₄×C₇	Dic₃	1	2	yes	direct product factor
15	C₂×C₃×C₄	C₂×C₇	1	1	yes	characteristic
16	C₂×Dic₃	C₂×C₇	1	2	yes	—
17	C₃×C₇	C₄²	1	1	yes	characteristic, complemented, Hall
18	C₄²	—	3	1	no	Sylow
19	C₂×C₇	C₄×D₃	1	2	yes	—
20	C₂×C₇	C₂×Dic₃	1	1	yes	characteristic
21	C₂²×C₃	C₂²×C₇	1	1	yes	characteristic
22	C₃×C₄	C₄×C₇	1	2	yes	complemented
23	Dic₃	C₄×C₇	1	4	yes	direct product factor
24	C₂×C₄	—	3	2	no	—
25	C₂×C₄	D₃×C₇	1	1	yes	characteristic
26	C₇	C₄×Dic₃	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₃	C₂×C₄×C₇	1	2	yes	—
28	C₂×C₃	C₂×C₄×C₇	1	1	yes	characteristic
29	C₂²	C₂×D₃×C₇	1	1	yes	characteristic
30	C₄	—	3	4	no	—
31	C₄	C₇×Dic₃	1	2	yes	direct product factor
32	C₃	C₄²×C₇	1	1	yes	characteristic, complemented, Sylow
33	C₂	C₄×D₃×C₇	1	2	yes	—
34	C₂	C₂×C₇×Dic₃	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.