Subgroups — #66365

Order 324.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic, complemented
2	C₂²⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
3	#1094	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₂²⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
5	#731	—	4	1	no	maximal, Sylow
6	C₂×3₋¹⁺²	—	3	1	no	—
7	C₂²×C₃²	C₃²	1	1	yes	characteristic
8	C₃×A₄	—	3	1	no	—
9	C₂²×C₉	—	3	1	no	—
10	C₂²⋊C₉	—	3	1	no	—
11	C₂²⋊C₉	—	3	1	no	—
12	3₋¹⁺²	—	4	1	no	—
13	3₋¹⁺²	A₄	1	1	yes	characteristic, complemented
14	H(3,𝔽₃)	—	4	1	no	—
15	C₃×C₉	—	4	1	no	—
16	C₂×C₃²	—	3	1	no	—
17	C₂×C₉	—	3	3	no	—
18	C₂²×C₃	—	3	1	no	—
19	C₂²×C₃	H(3,𝔽₃)	1	1	yes	characteristic
20	A₄	—	9	1	no	—
21	C₃²	—	12	1	no	—
22	C₃²	C₃×A₄	1	1	yes	characteristic
23	C₉	—	3	1	no	—
24	C₉	—	12	1	no	—
25	C₉	—	12	1	no	—
26	C₂×C₃	—	3	1	no	—
27	C₂×C₃	—	9	1	no	—
28	C₂²	#731	1	1	yes	characteristic, complemented, Sylow
29	C₃	—	3	1	no	—
30	C₃	—	36	1	no	—
31	C₃	C₂²⋊H(3,𝔽₃)	1	1	yes	characteristic
32	C₂	—	3	1	no	—

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.