Subgroups — C₃²×C₂²⋊(C₂²⋊A₄) #13181868

Order 1728.

6794 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁶×C₃²	C₃	1	1	yes	maximal, characteristic, complemented
2	C₃×C₂²⋊(C₂²⋊A₄)	C₃	1	12	yes	maximal, direct product factor
3	C₃²×C₂²⋊A₄	—	4	21	no	maximal
4	C₂⁵×C₃²	—	3	21	no	—
5	C₂⁶×C₃	C₃²	1	4	yes	complemented
6	C₂²⋊(C₂²⋊A₄)	C₃²	1	9	yes	direct product factor
7	C₂⁴×C₃²	—	3	210	no	—
8	C₂⁴×C₃²	A₄	1	21	yes	complemented
9	C₃×C₂²⋊A₄	—	4	252	no	—
10	C₃²×A₄	—	16	21	no	—
11	C₂⁵×C₃	—	3	84	no	—
12	C₂³×C₃²	—	3	360	no	—
13	C₂³×C₃²	—	3	105	no	—
14	C₂⁶	C₃³	1	1	yes	characteristic, complemented, Sylow
15	C₂⁴×C₃	—	3	840	no	—
16	C₂⁴×C₃	C₃×A₄	1	84	yes	complemented
17	C₂²⋊A₄	—	4	189	no	—
18	C₂²×C₃²	—	3	210	no	—
19	C₂²×C₃²	C₂²⋊A₄	1	21	yes	complemented
20	C₃×A₄	—	16	252	no	—
21	C₂⁵	—	3	21	no	—
22	C₃³	—	64	1	no	Sylow
23	C₂³×C₃	—	3	1440	no	—
24	C₂³×C₃	—	3	420	no	—
25	C₂×C₃²	—	3	21	no	—
26	C₂⁴	—	3	210	no	—
27	C₂⁴	C₃²×A₄	1	21	yes	complemented
28	C₂²×C₃	—	3	840	no	—
29	C₂²×C₃	C₃×C₂²⋊A₄	1	84	yes	complemented
30	A₄	—	16	189	no	—
31	C₃²	—	64	12	no	—
32	C₃²	C₂²⋊(C₂²⋊A₄)	1	1	yes	characteristic, direct product factor
33	C₂³	—	3	360	no	—
34	C₂³	—	3	105	no	—
35	C₂×C₃	—	3	84	no	—
36	C₂²	—	3	210	no	—
37	C₂²	C₃²×C₂²⋊A₄	1	21	yes	complemented
38	C₃	—	64	9	no	—
39	C₃	C₃×C₂²⋊(C₂²⋊A₄)	1	4	yes	direct product factor
40	C₂	—	3	21	no	—

	subgroup	G/H
center, hypercenter	C₃²	C₂²⋊(C₂²⋊A₄)
commutator, cosocle, hypocenter	C₂⁶	C₃³
Frattini	C₁	G
Fitting, socle	C₂⁶×C₃²	C₃
LCS	G ▷ C₂⁶
UCS	C₁ ◁ C₃²

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.