Subgroups — C₆₁⋊C₃×C₆₇⋊C₃ #49145448

Order 36783.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27133912	C₃	1	1	yes	maximal, characteristic, complemented
2	#27133911	C₃	1	1	yes	maximal, characteristic, complemented
3	C₆₁×C₆₇⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₆₇×C₆₁⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
5	C₆₁×C₆₇	C₃²	1	1	yes	characteristic, complemented, Hall
6	C₃×C₆₇⋊C₃	—	61	1	no	maximal, Hall
7	C₃×C₆₁⋊C₃	—	67	1	no	maximal, Hall
8	C₃×C₆₇	—	61	1	no	—
9	C₆₇⋊C₃	—	61	1	no	—
10	C₆₇⋊C₃	—	61	1	no	—
11	C₆₇⋊C₃	C₆₁⋊C₃	1	1	yes	characteristic, direct product factor
12	C₃×C₆₁	—	67	1	no	—
13	C₆₁⋊C₃	—	67	1	no	—
14	C₆₁⋊C₃	—	67	1	no	—
15	C₆₁⋊C₃	C₆₇⋊C₃	1	1	yes	characteristic, direct product factor
16	C₆₇	C₃×C₆₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
17	C₆₁	C₃×C₆₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
18	C₃²	—	4087	1	no	Sylow
19	C₃	—	61	1	no	—
20	C₃	—	67	1	no	—
21	C₃	—	4087	1	no	—
22	C₃	—	4087	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₆₁×C₆₇	C₃²
LCS	G ▷ C₆₁×C₆₇
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.