Subgroups — D₃×C₁₃₆₉⋊C₃ #37590191

Order 24642.

27 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃₆₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₁₃₆₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃₆₉⋊C₃	—	3	1	no	maximal
4	C₃×C₁₃₆₉	C₂×C₃	1	1	yes	characteristic, complemented
5	C₁₃₆₉⋊C₃	—	2	1	no	—
6	C₁₃₆₉⋊C₃	D₃	1	1	yes	characteristic, direct product factor
7	C₂×C₁₃₆₉	—	3	1	no	Hall
8	C₁₃₆₉	C₃×D₃	1	1	yes	characteristic, complemented, Sylow
9	D₃×C₃₇⋊C₃	—	37	1	no	maximal
10	C₃×C₃₇⋊C₃	—	37	1	no	—
11	D₃×C₃₇	C₃₇⋊C₃	1	1	yes	characteristic
12	C₂×C₃₇⋊C₃	—	111	1	no	—
13	C₃×C₃₇	C₂×C₃₇⋊C₃	1	1	yes	characteristic
14	C₃₇⋊C₃	—	37	1	no	—
15	C₃₇⋊C₃	—	74	1	no	—
16	C₂×C₃₇	—	3	1	no	—
17	C₃₇	D₃×C₃₇⋊C₃	1	1	yes	characteristic
18	C₃×D₃	—	1369	1	no	Hall
19	C₃²	—	1369	1	no	Sylow
20	C₂×C₃	—	4107	1	no	—
21	D₃	C₁₃₆₉⋊C₃	1	1	yes	characteristic, direct product factor
22	C₃	—	1369	1	no	—
23	C₃	—	2738	1	no	—
24	C₃	C₂×C₁₃₆₉⋊C₃	1	1	yes	characteristic, complemented
25	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃×C₁₃₆₉	C₂×C₃
Frattini	C₃₇	D₃×C₃₇⋊C₃
socle	C₃×C₃₇	C₂×C₃₇⋊C₃
LCS	G ▷ C₃×C₁₃₆₉
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.