Subgroups — C₃×#10596779 #13181840

Order 1728.

722 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂²⋊(C₂²⋊A₄)	C₃	1	1	yes	maximal, characteristic
2	#10596779	C₃	1	3	yes	maximal, direct product factor
3	C₂⁶×C₃	C₉	1	1	yes	characteristic, complemented
4	C₂²⋊(C₂²⋊A₄)	C₉	1	2	yes	complemented
5	C₂²⋊(C₂²⋊A₄)	C₃²	1	1	yes	characteristic
6	C₃×C₂²⋊A₄	—	12	7	no	—
7	C₂⁵×C₃	—	9	7	no	—
8	C₂⁶	C₃×C₉	1	1	yes	characteristic, complemented, Sylow
9	C₂⁴×C₃	—	3	7	no	—
10	C₂⁴×C₃	—	9	21	no	—
11	C₂⁴×C₃	—	9	7	no	—
12	C₂⁴×C₃	—	9	42	no	—
13	C₂²⋊A₄	—	12	14	no	—
14	C₂²⋊A₄	—	12	7	no	—
15	C₃×A₄	—	48	7	no	—
16	C₂⁵	—	9	7	no	—
17	C₃×C₉	—	64	1	no	maximal, Sylow
18	C₂³×C₃	—	9	14	no	—
19	C₂³×C₃	—	9	21	no	—
20	C₂³×C₃	—	9	21	no	—
21	C₂³×C₃	—	9	42	no	—
22	C₂³×C₃	—	9	42	no	—
23	C₂³×C₃	—	9	1	no	—
24	C₂³×C₃	—	9	14	no	—
25	C₂⁴	—	3	7	no	—
26	C₂⁴	—	9	21	no	—
27	C₂⁴	—	9	7	no	—
28	C₂⁴	—	9	42	no	—
29	C₂²×C₃	—	3	7	no	—
30	C₂²×C₃	—	9	21	no	—
31	C₂²×C₃	—	9	7	no	—
32	C₂²×C₃	—	9	42	no	—
33	A₄	—	48	7	no	—
34	A₄	—	48	14	no	—
35	C₃²	—	64	1	no	—
36	C₉	—	64	3	no	—
37	C₂³	—	9	14	no	—
38	C₂³	—	9	21	no	—
39	C₂³	—	9	21	no	—
40	C₂³	—	9	42	no	—
41	C₂³	—	9	42	no	—
42	C₂³	—	9	1	no	—
43	C₂³	—	9	14	no	—
44	C₂×C₃	—	9	7	no	—
45	C₂²	—	3	7	no	—
46	C₂²	—	9	21	no	—
47	C₂²	—	9	7	no	—
48	C₂²	—	9	42	no	—
49	C₃	—	64	1	no	—
50	C₃	—	64	2	no	—
51	C₃	#10596779	1	1	yes	characteristic, direct product factor
52	C₂	—	9	7	no	—

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.