Subgroups — D₇×3₋¹⁺² #67378

Order 378.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃²×D₇	C₃	1	1	yes	maximal, characteristic
3	C₉×D₇	C₃	1	3	yes	maximal, complemented
4	C₃²×C₇	C₂×C₃	1	1	yes	characteristic
5	C₇×C₉	C₂×C₃	1	3	yes	complemented
6	C₂×3₋¹⁺²	—	7	1	no	maximal, Hall
7	C₃×D₇	—	3	1	no	—
8	C₃×D₇	C₃²	1	1	yes	characteristic
9	3₋¹⁺²	D₇	1	1	yes	characteristic, direct product factor, Sylow
10	C₃×C₇	—	3	1	no	—
11	C₃×C₇	C₂×C₃²	1	1	yes	characteristic
12	C₂×C₃²	—	7	1	no	—
13	C₂×C₉	—	7	3	no	—
14	D₇	3₋¹⁺²	1	1	yes	characteristic, direct product factor, Hall
15	C₃²	C₃×D₇	1	1	yes	characteristic
16	C₉	C₃×D₇	1	3	yes	complemented
17	C₇	C₂×3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₃	—	7	1	no	—
19	C₂×C₃	—	21	1	no	—
20	C₃	—	3	1	no	—
21	C₃	C₃²×D₇	1	1	yes	characteristic
22	C₂	—	7	1	no	Sylow

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.