Subgroups — #41001913

Order 26888.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27212071	C₂	1	1	yes	maximal, characteristic
2	D₃₃₆₁	C₄	1	1	yes	characteristic
3	C₃₃₆₁	C₈	1	1	yes	characteristic, complemented, Sylow
4	C₈	—	3361	1	no	maximal, Sylow
5	C₄	—	3361	1	no	—
6	C₂	—	3361	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃₃₆₁	C₈
prime radical	D₃₃₆₁	C₄
cosocle	#27212071	C₂
LCS	G ▷ C₃₃₆₁
UCS	C₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₃₃₆₁	C₈	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#27212071	2
C₈	3361