Subgroups — #29503775⋊C₂ #44478708

Order 30474.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#29503775	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₆₉₃⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₁₆₉₃⋊C₃	C₂×C₃	1	1	yes	characteristic
4	D₁₆₉₃	C₉	1	1	yes	characteristic, complemented, Hall
5	C₁₆₉₃	C₂×C₉	1	1	yes	characteristic, complemented, Sylow
6	C₂×C₉	—	1693	1	no	maximal, Hall
7	C₉	—	1693	1	no	Sylow
8	C₂×C₃	—	1693	1	no	—
9	C₃	—	1693	1	no	—
10	C₂	—	15237	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₆₉₃	C₂×C₉
prime radical	D₁₆₉₃⋊C₃	C₃
cosocle	C₁₆₉₃⋊C₃	C₂×C₃
LCS	G ▷ C₁₆₉₃
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.