Subgroups — C₃²×#10587020 #17987592

Order 4617.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#10587020	C₃	1	12	yes	maximal, direct product factor
2	C₃²×#4294	C₃	1	1	yes	maximal, characteristic
3	C₃³×C₁₉	C₉	1	1	yes	characteristic
4	C₃×#4294	C₉	1	8	yes	—
5	C₃×#4294	C₃²	1	4	yes	—
6	#10587020	C₃²	1	9	yes	direct product factor
7	C₃²×C₂₇	—	19	1	no	maximal, Sylow
8	C₃²×C₁₉	C₂₇	1	9	yes	complemented
9	C₃²×C₁₉	C₃×C₉	1	4	yes	—
10	#4294	C₃×C₉	1	8	yes	—
11	#4294	C₃³	1	1	yes	characteristic
12	C₃²×C₉	—	19	1	no	—
13	C₃×C₂₇	—	19	12	no	—
14	C₃×C₁₉	C₃×C₂₇	1	12	yes	complemented
15	C₃×C₁₉	C₃²×C₉	1	1	yes	characteristic
16	C₃³	#4296	1	1	yes	characteristic
17	C₃×C₉	—	19	8	no	—
18	C₃×C₉	—	19	4	no	—
19	C₂₇	—	19	9	no	—
20	C₁₉	C₃²×C₂₇	1	1	yes	characteristic, complemented, Sylow
21	C₃²	#10587020	1	9	yes	direct product factor
22	C₃²	C₃×#4296	1	4	yes	—
23	C₉	—	19	1	no	—
24	C₉	—	19	8	no	—
25	C₃	C₃×#10587020	1	12	yes	direct product factor
26	C₃	C₃²×#4296	1	1	yes	characteristic

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.