Subgroups — C₃×C₉²×C₆₁ #28414985

Order 14823.

252 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₉×C₆₁	C₃	1	4	yes	maximal
2	C₉²×C₆₁	C₃	1	9	yes	maximal, direct product factor
3	C₃³×C₆₁	C₃²	1	1	yes	characteristic
4	C₃×C₉×C₆₁	C₉	1	36	yes	direct product factor
5	C₃×C₉×C₆₁	C₃²	1	12	yes	—
6	C₃²×C₆₁	C₃×C₉	1	12	yes	—
7	C₃²×C₆₁	C₃³	1	1	yes	characteristic
8	C₉×C₆₁	C₃×C₉	1	36	yes	direct product factor
9	C₃×C₉²	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₃×C₆₁	C₉²	1	9	yes	direct product factor
11	C₃×C₆₁	C₃²×C₉	1	4	yes	—
12	C₃²×C₉	C₃×C₆₁	1	4	yes	—
13	C₉²	C₃×C₆₁	1	9	yes	direct product factor
14	C₆₁	C₃×C₉²	1	1	yes	characteristic, direct product factor, Sylow
15	C₃³	C₃²×C₆₁	1	1	yes	characteristic
16	C₃×C₉	C₉×C₆₁	1	36	yes	direct product factor
17	C₃×C₉	C₃²×C₆₁	1	12	yes	—
18	C₃²	C₃×C₉×C₆₁	1	12	yes	—
19	C₃²	C₃³×C₆₁	1	1	yes	characteristic
20	C₉	C₃×C₉×C₆₁	1	36	yes	direct product factor
21	C₃	C₉²×C₆₁	1	9	yes	direct product factor
22	C₃	C₃²×C₉×C₆₁	1	4	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.