Subgroups — D₇⋊H(3,𝔽₃) #67359

Order 378.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇⋊H(3,𝔽₃)	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃²×D₇	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×AGL(1,𝔽₇)	C₃	1	3	yes	maximal, complemented
4	C₃²×C₇	C₂×C₃	1	1	yes	characteristic, complemented
5	C₃×ΓL(1,𝔽₈)	C₂×C₃	1	3	yes	complemented
6	C₂×H(3,𝔽₃)	—	7	1	no	maximal, Hall
7	C₃×D₇	—	3	1	no	—
8	C₃×D₇	C₃²	1	1	yes	characteristic
9	AGL(1,𝔽₇)	—	3	3	no	—
10	H(3,𝔽₃)	—	7	1	no	Sylow
11	C₃×C₇	—	3	1	no	—
12	C₃×C₇	C₂×C₃²	1	1	yes	characteristic
13	ΓL(1,𝔽₈)	—	3	3	no	—
14	C₂×C₃²	—	7	3	no	—
15	C₂×C₃²	—	7	1	no	—
16	D₇	H(3,𝔽₃)	1	1	yes	characteristic, complemented, Hall
17	C₃²	—	7	3	no	—
18	C₃²	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
19	C₇	C₂×H(3,𝔽₃)	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₃	—	7	1	no	—
21	C₂×C₃	—	21	1	no	—
22	C₂×C₃	—	21	3	no	—
23	C₃	—	3	1	no	—
24	C₃	—	21	3	no	—
25	C₃	C₃×AGL(1,𝔽₇)	1	1	yes	characteristic
26	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.