Subgroups — C₃²⋊(#564⋊C₃) #13152270

Order 1728.

244 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#564	C₃	1	1	yes	maximal, characteristic, complemented
2	C₃×#564⋊C₃	C₃	1	3	yes	maximal, complemented
3	C₃²⋊(C₄²⋊C₃)	—	4	5	no	maximal
4	C₃²×#125	—	3	5	no	—
5	C₃×#564	—	3	1	no	—
6	C₃×#564	C₃²	1	1	yes	characteristic
7	#564⋊C₃	—	3	3	no	—
8	C₃²×C₄⋊C₄	—	3	10	no	—
9	C₃²×C₄²	A₄	1	5	yes	—
10	C₃×C₄²⋊C₃	—	4	15	no	—
11	C₂²⋊H(3,𝔽₃)	—	16	1	no	—
12	C₃×#125	—	3	15	no	—
13	C₃×#125	—	3	5	no	—
14	C₂×C₃²×C₄	—	3	5	no	—
15	#564	H(3,𝔽₃)	1	1	yes	characteristic, complemented, Sylow
16	C₃×C₄⋊C₄	—	3	30	no	—
17	C₃×C₄⋊C₄	—	3	10	no	—
18	C₃×C₄²	—	3	5	no	—
19	C₃×C₄²	C₃×A₄	1	5	yes	—
20	C₄²⋊C₃	—	12	15	no	—
21	C₂²×C₃²	C₂²⋊A₄	1	1	yes	characteristic
22	C₃×A₄	—	16	3	no	—
23	C₃²×C₄	—	6	5	no	—
24	#125	—	3	5	no	—
25	H(3,𝔽₃)	—	64	1	no	Sylow
26	C₂×C₃×C₄	—	3	15	no	—
27	C₂×C₃×C₄	—	3	5	no	—
28	C₂×C₃²	—	3	1	no	—
29	C₄⋊C₄	—	3	10	no	—
30	C₄²	C₂²⋊H(3,𝔽₃)	1	5	yes	—
31	C₂²×C₃	—	3	1	no	—
32	C₂²×C₃	C₃×C₂²⋊A₄	1	1	yes	characteristic
33	A₄	—	48	3	no	—
34	C₃×C₄	—	6	15	no	—
35	C₃×C₄	—	6	5	no	—
36	C₃²	—	64	3	no	—
37	C₃²	#564⋊C₃	1	1	yes	characteristic, complemented
38	C₂×C₄	—	3	5	no	—
39	C₂×C₃	—	3	3	no	—
40	C₂×C₃	—	3	1	no	—
41	C₂²	C₃²⋊(C₂²⋊A₄)	1	1	yes	characteristic
42	C₄	—	6	5	no	—
43	C₃	—	3	1	no	—
44	C₃	—	192	3	no	—
45	C₃	C₃×#564⋊C₃	1	1	yes	characteristic
46	C₂	—	3	1	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.