Subgroups — #67356

Order 378.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#4427	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×AGL(1,𝔽₇)	C₃	1	1	yes	maximal, characteristic
3	C₉×D₇	C₃	1	1	yes	maximal, characteristic, complemented
4	D₇⋊C₉	C₃	1	2	yes	maximal, complemented
5	C₃×ΓL(1,𝔽₈)	C₂×C₃	1	1	yes	characteristic
6	C₇×C₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₇⋊C₉	C₂×C₃	1	2	yes	complemented
8	C₂×3₋¹⁺²	—	7	1	no	maximal, Hall
9	C₃×D₇	C₃²	1	1	yes	characteristic
10	AGL(1,𝔽₇)	—	3	1	no	—
11	3₋¹⁺²	—	7	1	no	Sylow
12	C₃×C₇	C₂×C₃²	1	1	yes	characteristic
13	ΓL(1,𝔽₈)	—	3	1	no	—
14	C₂×C₃²	—	7	1	no	—
15	C₂×C₉	—	7	2	no	—
16	C₂×C₉	—	7	1	no	—
17	D₇	3₋¹⁺²	1	1	yes	characteristic, complemented, Hall
18	C₃²	—	7	1	no	—
19	C₉	—	7	2	no	—
20	C₉	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
21	C₇	C₂×3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₃	—	7	1	no	—
23	C₂×C₃	—	21	1	no	—
24	C₃	—	21	1	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.