Subgroups — #23782751

Order 10449.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812513	C₃	1	3	yes	maximal, complemented
2	C₉²×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃²⋊(C₄₃⋊C₃)	—	3	3	no	—
4	C₃×C₉×C₄₃	—	3	1	no	—
5	C₃×C₉×C₄₃	C₃²	1	1	yes	characteristic
6	C₃²×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
7	C₃×C₄₃⋊C₃	—	9	3	no	—
8	C₉×C₄₃	—	3	3	no	—
9	C₉×C₄₃	—	3	1	no	—
10	#6879	—	43	1	no	maximal, Sylow
11	C₃×C₄₃	—	3	1	no	—
12	C₃×C₄₃	#732	1	1	yes	characteristic
13	C₄₃⋊C₃	—	27	3	no	—
14	#732	—	43	3	no	—
15	C₉²	C₄₃⋊C₃	1	1	yes	characteristic, complemented
16	C₄₃	#6879	1	1	yes	characteristic, complemented, Sylow
17	H(3,𝔽₃)	—	129	3	no	—
18	C₃×C₉	—	3	1	no	—
19	C₃×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
20	C₃²	—	387	3	no	—
21	C₃²	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
22	C₉	—	3	3	no	—
23	C₉	—	3	1	no	—
24	C₃	—	3	1	no	—
25	C₃	—	1161	3	no	—
26	C₃	#16812513	1	1	yes	characteristic

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