Subgroups — D₃×C₉² #92247

Order 486.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉²	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃×D₃×C₉	C₃	1	4	yes	maximal
3	C₂×C₉²	—	3	1	no	maximal
4	C₃²×C₉	C₂×C₃	1	4	yes	—
5	C₉²	—	2	4	no	—
6	C₉²	D₃	1	1	yes	characteristic, direct product factor
7	C₃²×D₃	C₃²	1	1	yes	characteristic
8	C₂×C₃×C₉	—	3	4	no	—
9	D₃×C₉	C₉	1	12	yes	direct product factor
10	C₃³	C₂×C₃²	1	1	yes	characteristic
11	C₃×C₉	—	2	4	no	—
12	C₃×C₉	—	2	12	no	—
13	C₃×C₉	C₂×C₉	1	12	yes	complemented
14	C₃×C₉	C₃×D₃	1	4	yes	—
15	C₂×C₃²	—	3	1	no	—
16	C₃×D₃	C₃×C₉	1	4	yes	—
17	C₂×C₉	—	3	12	no	—
18	C₃²	—	2	4	no	—
19	C₃²	C₂×C₃×C₉	1	4	yes	—
20	C₃²	C₃²×D₃	1	1	yes	characteristic
21	C₉	—	2	12	no	—
22	C₉	D₃×C₉	1	12	yes	direct product factor
23	C₂×C₃	—	3	4	no	—
24	D₃	C₉²	1	1	yes	characteristic, direct product factor
25	C₃	—	2	4	no	—
26	C₃	C₂×C₉²	1	1	yes	characteristic, complemented
27	C₃	C₃×D₃×C₉	1	4	yes	—
28	C₂	—	3	1	no	Sylow

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.