Subgroups — #66368

Order 324.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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