Subgroups — C₃×D₇⋊C₉ #67357

Order 378.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃²×D₇	C₃	1	1	yes	maximal, characteristic
3	D₇⋊C₉	C₃	1	3	yes	maximal, direct product factor
4	C₃²×C₇	C₂×C₃	1	1	yes	characteristic
5	C₇⋊C₉	C₂×C₃	1	3	yes	complemented
6	C₂×C₃×C₉	—	7	1	no	maximal, Hall
7	C₃×D₇	C₉	1	3	yes	complemented
8	C₃×D₇	C₃²	1	1	yes	characteristic
9	C₃×C₉	—	7	1	no	Sylow
10	C₃×C₇	C₂×C₉	1	3	yes	complemented
11	C₃×C₇	C₂×C₃²	1	1	yes	characteristic
12	C₂×C₃²	—	7	1	no	—
13	C₂×C₉	—	7	3	no	—
14	D₇	C₃×C₉	1	1	yes	characteristic, complemented, Hall
15	C₃²	AGL(1,𝔽₇)	1	1	yes	characteristic
16	C₉	—	7	3	no	—
17	C₇	C₂×C₃×C₉	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₃	—	7	3	no	—
19	C₂×C₃	—	7	1	no	—
20	C₃	D₇⋊C₉	1	3	yes	direct product factor
21	C₃	C₃×AGL(1,𝔽₇)	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.