Subgroups — C₃×#16812515 #23782872

Order 10449.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#11923958	C₃	1	3	yes	maximal
2	#16812515	C₃	1	9	yes	maximal, direct product factor
3	C₃²×C₉×C₄₃	C₃	1	1	yes	maximal, characteristic
4	#11923958	—	3	6	no	—
5	#11923958	C₃²	1	9	yes	—
6	C₃×C₄₃⋊C₉	—	3	3	no	—
7	C₃³×C₄₃	C₃²	1	1	yes	characteristic
8	C₃×C₉×C₄₃	—	3	2	no	—
9	C₃×C₉×C₄₃	—	3	1	no	—
10	C₃×C₉×C₄₃	C₃²	1	3	yes	—
11	C₃²×C₄₃	—	3	3	no	—
12	C₃²×C₄₃	H(3,𝔽₃)	1	2	yes	—
13	C₃²×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
14	C₃²×C₄₃	C₃³	1	1	yes	characteristic
15	C₉×C₄₃	—	3	3	no	—
16	C₄₃⋊C₉	—	3	9	no	—
17	C₃×#733	—	43	1	no	maximal, Sylow
18	C₃×C₄₃	—	3	2	no	—
19	C₃×C₄₃	—	3	1	no	—
20	C₃×C₄₃	#733	1	3	yes	complemented
21	C₃×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
22	C₃×3₋¹⁺²	—	43	3	no	—
23	C₃²×C₉	C₄₃⋊C₃	1	1	yes	characteristic
24	#733	—	43	9	no	—
25	C₄₃	C₃×#733	1	1	yes	characteristic, complemented, Sylow
26	C₃³	C₃×C₄₃⋊C₃	1	1	yes	characteristic
27	3₋¹⁺²	—	43	9	no	—
28	3₋¹⁺²	—	129	6	no	—
29	C₃×C₉	—	3	2	no	—
30	C₃×C₉	—	3	1	no	—
31	C₃×C₉	—	129	3	no	—
32	C₃×C₉	C₃×C₄₃⋊C₃	1	3	yes	—
33	C₃²	—	3	3	no	—
34	C₃²	C₃²⋊(C₄₃⋊C₃)	1	2	yes	—
35	C₃²	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
36	C₃²	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
37	C₉	—	3	3	no	—
38	C₉	—	129	9	no	—
39	C₃	—	3	2	no	—
40	C₃	—	3	1	no	—
41	C₃	#16812515	1	3	yes	direct product factor
42	C₃	C₃×C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.