Subgroups — #13048172

Order 1296.

312 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃×C₉	C₃	1	1	yes	maximal, characteristic, complemented
2	C₃²⋊(C₂²⋊A₄)	C₃	1	3	yes	maximal, complemented
3	#66358	—	4	5	no	maximal
4	C₂³×C₃×C₉	—	3	5	no	—
5	C₂⁴×C₃²	C₃²	1	1	yes	characteristic
6	C₃×C₂²⋊A₄	—	3	3	no	—
7	C₂⁴×C₉	—	3	1	no	—
8	C₂²×C₃×C₉	—	3	10	no	—
9	C₂²×C₃×C₉	A₄	1	5	yes	complemented
10	C₂²⋊H(3,𝔽₃)	—	4	15	no	—
11	#732	—	16	1	no	Sylow
12	C₂³×C₃²	—	3	5	no	—
13	C₂³×C₉	—	3	15	no	—
14	C₂×C₃×C₉	—	3	5	no	—
15	C₂⁴×C₃	—	3	1	no	—
16	C₂⁴×C₃	H(3,𝔽₃)	1	1	yes	characteristic
17	C₂²⋊A₄	—	9	3	no	—
18	C₂²×C₃²	—	3	10	no	—
19	C₂²×C₃²	C₃×A₄	1	5	yes	—
20	C₃×A₄	—	12	15	no	—
21	C₂²×C₉	—	3	30	no	—
22	C₂²×C₉	—	3	5	no	—
23	H(3,𝔽₃)	—	16	3	no	—
24	C₃×C₉	C₂²⋊A₄	1	1	yes	characteristic, complemented
25	C₂³×C₃	—	3	15	no	—
26	C₂³×C₃	—	3	5	no	—
27	C₂×C₃²	—	3	5	no	—
28	C₂×C₉	—	3	15	no	—
29	C₂⁴	#732	1	1	yes	characteristic, complemented, Sylow
30	C₂²×C₃	—	3	10	no	—
31	C₂²×C₃	—	3	30	no	—
32	C₂²×C₃	—	3	5	no	—
33	C₂²×C₃	C₂²⋊H(3,𝔽₃)	1	5	yes	—
34	A₄	—	36	15	no	—
35	C₃²	—	48	3	no	—
36	C₃²	C₃×C₂²⋊A₄	1	1	yes	characteristic
37	C₉	—	3	1	no	—
38	C₂³	—	3	5	no	—
39	C₂×C₃	—	3	15	no	—
40	C₂×C₃	—	3	5	no	—
41	C₂²	—	3	10	no	—
42	C₂²	#66358	1	5	yes	complemented
43	C₃	—	3	1	no	—
44	C₃	—	144	3	no	—
45	C₃	C₃²⋊(C₂²⋊A₄)	1	1	yes	characteristic
46	C₂	—	3	5	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.