Subgroups — #66366

Order 324.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×A₄	C₃	1	1	yes	maximal, characteristic, complemented
2	C₂²×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic, complemented
4	#1094	C₃	1	1	yes	maximal, characteristic, complemented
5	AΣL(1,𝔽₂₇)	—	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	C₃×A₄	—	3	3	no	—
10	C₃×A₄	—	3	1	no	—
11	C₂²×C₉	—	3	1	no	—
12	C₂²⋊C₉	—	3	1	no	—
13	C₃³	—	4	1	no	—
14	3₋¹⁺²	—	4	1	no	—
15	3₋¹⁺²	A₄	1	1	yes	characteristic, complemented
16	H(3,𝔽₃)	—	4	1	no	—
17	C₂×C₃²	—	3	1	no	—
18	C₂×C₉	—	3	3	no	—
19	C₂²×C₃	—	3	1	no	—
20	C₂²×C₃	H(3,𝔽₃)	1	1	yes	characteristic
21	A₄	—	3	3	no	—
22	A₄	—	9	1	no	—
23	C₃²	—	12	3	no	—
24	C₃²	—	12	1	no	—
25	C₃²	—	12	1	no	—
26	C₃²	C₃×A₄	1	1	yes	characteristic
27	C₉	—	3	1	no	—
28	C₉	—	12	1	no	—
29	C₂×C₃	—	3	1	no	—
30	C₂×C₃	—	9	1	no	—
31	C₂²	AΣL(1,𝔽₂₇)	1	1	yes	characteristic, complemented, Sylow
32	C₃	—	3	1	no	—
33	C₃	—	12	3	no	—
34	C₃	—	36	1	no	—
35	C₃	C₂²⋊H(3,𝔽₃)	1	1	yes	characteristic
36	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.