Subgroups — #88586

Order 432.

21 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6188	C₂	1	1	yes	maximal, characteristic
2	#1084	C₄	1	1	yes	characteristic
3	C₂×H(3,𝔽₃)	C₈	1	1	yes	characteristic
4	C₃⋊C₁₆	—	9	1	no	maximal
5	C₃×Dic₃	—	12	1	no	—
6	H(3,𝔽₃)	C₁₆	1	1	yes	characteristic, complemented, Sylow
7	C₃×C₈	—	9	1	no	—
8	C₂×C₃²	—	4	1	no	—
9	C₁₆	—	27	1	no	Sylow
10	C₃×C₄	—	9	1	no	—
11	Dic₃	—	12	1	no	—
12	C₃²	—	4	1	no	—
13	C₈	—	9	1	no	—
14	C₂×C₃	—	12	1	no	—
15	C₂×C₃	AGL(1,𝔽₉)	1	1	yes	characteristic
16	C₄	—	9	1	no	—
17	C₃	—	12	1	no	—
18	C₃	#3771	1	1	yes	characteristic
19	C₂	#6249	1	1	yes	characteristic

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

N	H ≅ G/N	type
6. H(3,𝔽₃)	C₁₆	semidirect

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

subgroup	index
#6188	2
C₃⋊C₁₆	9