Subgroups — C₃²⋊#13184224 #30633124

Order 16119.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13184224	C₃	1	3	yes	maximal, complemented
2	C₃³×C₁₉₉	C₃	1	1	yes	maximal, characteristic
3	C₃²×C₁₉₉	—	3	1	no	—
4	C₃²×C₁₉₉	—	3	2	no	—
5	C₃²×C₁₉₉	C₉	1	3	yes	complemented
6	C₃²×C₁₉₉	C₃²	1	1	yes	characteristic
7	#13184224	—	3	3	no	—
8	C₃×C₁₉₉	—	3	3	no	—
9	C₃×C₁₉₉	C₃×C₉	1	1	yes	characteristic
10	C₃×C₁₉₉	H(3,𝔽₃)	1	1	yes	characteristic
11	C₃×C₁₉₉	3₋¹⁺²	1	2	yes	—
12	C₁₉₉	C₃²⋊C₉	1	1	yes	characteristic, complemented, Sylow
13	C₃²⋊C₉	—	199	1	no	maximal, Sylow
14	C₃³	C₁₉₉⋊C₃	1	1	yes	characteristic
15	C₃×C₉	—	199	3	no	—
16	C₃²	—	3	1	no	—
17	C₃²	—	3	2	no	—
18	C₃²	#13184224	1	3	yes	complemented
19	C₃²	C₃×C₁₉₉⋊C₃	1	1	yes	characteristic
20	C₉	—	597	3	no	—
21	C₃	—	3	3	no	—
22	C₃	C₃×#13184224	1	1	yes	characteristic
23	C₃	C₃²⋊(C₁₉₉⋊C₃)	1	1	yes	characteristic
24	C₃	#19129017	1	2	yes	—

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.