Subgroups — C₃⋊(C₇⋊D₇) #64433

Order 294.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇⋊D₇	—	3	1	no	maximal, Hall
3	C₇²	D₃	1	1	yes	characteristic, complemented, Sylow
4	D₂₁	—	7	8	no	maximal
5	C₃×C₇	D₇	1	8	yes	complemented
6	D₇	—	21	8	no	—
7	C₇	D₂₁	1	8	yes	complemented
8	D₃	—	49	1	no	Hall
9	C₃	C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
10	C₂	—	147	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇²	C₂
LCS	G ▷ C₃×C₇²
UCS	C₁

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.