Subgroups — #30633162

Order 16119.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19129019	C₃	1	3	yes	maximal, complemented
2	C₃×#13184224	C₃	1	1	yes	maximal, characteristic
3	C₃²×C₁₉₉	C₉	1	1	yes	characteristic
4	#13184224	C₉	1	2	yes	—
5	#13184224	C₃²	1	1	yes	characteristic
6	C₃×C₁₉₉	—	3	1	no	—
7	C₃×C₁₉₉	C₃×C₉	1	1	yes	characteristic
8	C₁₉₉	C₂₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
9	C₂₇⋊C₃	—	199	1	no	maximal, Sylow
10	C₃×C₉	—	199	1	no	—
11	C₂₇	—	199	3	no	—
12	C₃²	#13184226	1	1	yes	characteristic
13	C₉	—	199	1	no	—
14	C₉	—	199	2	no	—
15	C₃	—	3	1	no	—
16	C₃	C₃×#13184226	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #19129019	C₃	semidirect
8. C₁₉₉	C₂₇⋊C₃	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.