Subgroups — #23782736

Order 10449.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812505	C₃	1	2	yes	maximal
2	#16812499	C₃	1	1	yes	maximal, characteristic
3	C₄₃×C₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic
4	C₃×C₄₃⋊C₉	—	3	1	no	—
5	C₄₃⋊C₂₇	—	3	2	no	—
6	C₃×C₉×C₄₃	C₃²	1	1	yes	characteristic
7	C₂₇×C₄₃	C₉	1	3	yes	complemented
8	C₃²×C₄₃	3₋¹⁺²	1	1	yes	characteristic
9	C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
10	C₉×C₄₃	3₋¹⁺²	1	2	yes	—
11	C₄₃⋊C₉	—	9	1	no	—
12	#6875	—	43	1	no	maximal, Sylow
13	C₃×C₄₃	—	3	1	no	—
14	C₃×C₄₃	C₉⋊C₉	1	1	yes	characteristic
15	C₂₇⋊C₃	—	43	2	no	—
16	C₂₇⋊C₃	C₄₃⋊C₃	1	1	yes	characteristic
17	C₉⋊C₉	—	43	1	no	—
18	C₄₃	#6875	1	1	yes	characteristic, complemented, Sylow
19	C₃×C₉	—	129	1	no	—
20	C₃×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
21	C₂₇	—	129	2	no	—
22	C₂₇	C₄₃⋊C₉	1	3	yes	complemented
23	C₃²	#11923957	1	1	yes	characteristic
24	C₉	—	387	1	no	—
25	C₉	C₃×C₄₃⋊C₉	1	1	yes	characteristic
26	C₉	#11923957	1	2	yes	—
27	C₃	—	3	1	no	—
28	C₃	#16812499	1	1	yes	characteristic

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