Subgroups — #13049337

Order 1296.

451 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
2	#88907	C₃	1	8	yes	maximal, complemented
3	C₃×C₂²⋊(C₂²⋊C₉)	C₃	1	4	yes	maximal, complemented
4	#66437	—	4	5	no	maximal
5	C₂³×H(3,𝔽₃)	—	3	5	no	—
6	C₂⁴×C₃²	C₃²	1	4	yes	—
7	C₂²⋊(C₂²⋊C₉)	C₃²	1	1	yes	characteristic
8	C₂²⋊(C₂²⋊C₉)	C₃²	1	8	yes	—
9	C₂²×H(3,𝔽₃)	—	3	10	no	—
10	C₂²×H(3,𝔽₃)	A₄	1	5	yes	—
11	#1094	—	4	40	no	—
12	C₃×C₂²⋊C₉	—	4	20	no	—
13	#737	—	16	1	no	Sylow
14	C₂³×C₃²	—	3	20	no	—
15	C₂×H(3,𝔽₃)	—	3	5	no	—
16	C₂⁴×C₃	—	3	4	no	—
17	C₂⁴×C₃	C₃³	1	1	yes	characteristic
18	C₂²×C₃²	—	3	40	no	—
19	C₂²×C₃²	C₃×A₄	1	20	yes	—
20	C₂²⋊C₉	—	4	5	no	—
21	C₂²⋊C₉	—	4	40	no	—
22	3₋¹⁺²	—	16	8	no	—
23	H(3,𝔽₃)	C₂²⋊A₄	1	1	yes	characteristic
24	C₃×C₉	—	16	4	no	—
25	C₂³×C₃	—	3	5	no	—
26	C₂³×C₃	—	9	20	no	—
27	C₂×C₃²	—	3	20	no	—
28	C₂⁴	#737	1	1	yes	characteristic, complemented, Sylow
29	C₂²×C₃	—	3	10	no	—
30	C₂²×C₃	—	3	20	no	—
31	C₂²×C₃	—	9	40	no	—
32	C₂²×C₃	C₃²×A₄	1	5	yes	—
33	C₃²	C₃×C₂²⋊A₄	1	4	yes	—
34	C₉	—	16	1	no	—
35	C₉	—	16	8	no	—
36	C₂³	—	3	5	no	—
37	C₂×C₃	—	3	5	no	—
38	C₂×C₃	—	9	20	no	—
39	C₂²	—	3	10	no	—
40	C₂²	#66437	1	5	yes	complemented
41	C₃	—	3	4	no	—
42	C₃	C₃²×C₂²⋊A₄	1	1	yes	characteristic
43	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.