Subgroups — #14516413

Order 1944.

53 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11757369	C₂	1	3	yes	maximal
2	#92197	C₂²	1	1	yes	characteristic
3	#6855	Q₈	1	1	yes	characteristic, complemented, Sylow
4	C₃×PSU(3,𝔽₂)	—	9	1	no	maximal
5	C₃×C₃⋊D₉	—	12	1	no	—
6	C₃×#157	—	9	3	no	—
7	C₃²×C₉	—	4	1	no	—
8	PSU(3,𝔽₂)	—	9	1	no	—
9	C₃×C₃⋊D₃	—	9	1	no	—
10	C₃⋊D₉	—	12	1	no	—
11	C₃×D₉	—	36	3	no	—
12	#157	—	9	3	no	—
13	C₃³	PSU(3,𝔽₂)	1	1	yes	characteristic
14	C₃×C₉	—	4	3	no	—
15	C₃×C₉	—	12	1	no	—
16	C₃×C₉	—	24	1	no	—
17	C₃×Q₈	—	81	1	no	—
18	C₃⋊D₃	—	9	1	no	—
19	C₃×D₃	—	108	1	no	—
20	D₉	—	36	3	no	—
21	C₃×C₄	—	81	3	no	—
22	C₃²	—	4	1	no	—
23	C₃²	—	8	1	no	—
24	C₃²	SU(3,𝔽₂)	1	1	yes	characteristic
25	C₉	—	12	3	no	—
26	Q₈	—	81	1	no	Sylow
27	C₂×C₃	—	81	1	no	—
28	D₃	—	108	1	no	—
29	C₄	—	81	3	no	—
30	C₃	—	4	1	no	—
31	C₃	—	8	1	no	—
32	C₃	#10619734	1	1	yes	characteristic
33	C₂	—	81	1	no	—

	subgroup	G/H
center, hypercenter	C₃	#10619734
commutator, prime radical, cosocle	#92197	C₂²
Frattini, socle	C₃³	PSU(3,𝔽₂)
Fitting, hypocenter	#6855	Q₈
LCS	G ▷ #92197 ▷ #6855
UCS	C₁ ◁ C₃

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

N	H ≅ G/N	type
3. #6855	Q₈	semidirect

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

subgroup	index
#11757369	2
C₃×PSU(3,𝔽₂)	9