Subgroups — #39906237

Order 25929.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₃×C₆₇	C₃	1	1	yes	maximal, characteristic
2	C₄₃×C₆₇	C₉	1	1	yes	characteristic, complemented, Hall
3	C₆₇⋊C₉	—	43	1	no	maximal, Hall
4	C₄₃⋊C₉	—	67	1	no	maximal, Hall
5	C₃×C₆₇	C₄₃⋊C₃	1	1	yes	characteristic
6	C₃×C₄₃	C₆₇⋊C₃	1	1	yes	characteristic
7	C₆₇	C₄₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
8	C₄₃	C₆₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
9	C₉	—	2881	1	no	Sylow
10	C₃	#22575686	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₃	#22575686
commutator, hypocenter	C₄₃×C₆₇	C₉
Fitting, socle, prime radical, cosocle	C₃×C₄₃×C₆₇	C₃
LCS	G ▷ C₄₃×C₆₇
UCS	C₁ ◁ C₃

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.