Subgroups — #66358

Order 324.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₉	C₃	1	1	yes	maximal, characteristic, complemented
2	C₂²⋊H(3,𝔽₃)	C₃	1	3	yes	maximal, complemented
3	#732	—	4	1	no	maximal, Sylow
4	C₂×C₃×C₉	—	3	1	no	—
5	C₂²×C₃²	C₃²	1	1	yes	characteristic
6	C₃×A₄	—	3	3	no	—
7	C₂²×C₉	—	3	1	no	—
8	H(3,𝔽₃)	—	4	3	no	—
9	C₃×C₉	A₄	1	1	yes	characteristic, complemented
10	C₂×C₃²	—	3	1	no	—
11	C₂×C₉	—	3	3	no	—
12	C₂²×C₃	—	3	1	no	—
13	C₂²×C₃	H(3,𝔽₃)	1	1	yes	characteristic
14	A₄	—	9	3	no	—
15	C₃²	—	12	3	no	—
16	C₃²	C₃×A₄	1	1	yes	characteristic
17	C₉	—	3	1	no	—
18	C₂×C₃	—	3	3	no	—
19	C₂×C₃	—	3	1	no	—
20	C₂²	#732	1	1	yes	characteristic, complemented, Sylow
21	C₃	—	3	1	no	—
22	C₃	—	36	3	no	—
23	C₃	C₂²⋊H(3,𝔽₃)	1	1	yes	characteristic
24	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.