Subgroups — #10619575

Order 648.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Q₈×C₉	C₃	1	1	yes	maximal, characteristic, complemented
2	Q₈⋊H(3,𝔽₃)	C₃	1	3	yes	maximal, complemented
3	C₂×#732	—	4	1	no	maximal
4	C₃×C₄×C₉	—	3	1	no	—
5	#732	—	4	1	no	Sylow
6	C₃²×Q₈	C₃²	1	1	yes	characteristic
7	C₃×SL(2,𝔽₃)	—	3	3	no	—
8	Q₈×C₉	—	3	1	no	—
9	C₂×H(3,𝔽₃)	—	4	3	no	—
10	C₂×C₃×C₉	A₄	1	1	yes	characteristic
11	C₃²×C₄	—	3	1	no	—
12	C₄×C₉	—	3	3	no	—
13	H(3,𝔽₃)	—	4	3	no	—
14	C₃×C₉	SL(2,𝔽₃)	1	1	yes	characteristic, complemented
15	C₃×Q₈	—	3	1	no	—
16	C₃×Q₈	H(3,𝔽₃)	1	1	yes	characteristic
17	SL(2,𝔽₃)	—	9	3	no	—
18	C₂×C₃²	—	12	3	no	—
19	C₂×C₃²	C₃×A₄	1	1	yes	characteristic
20	C₂×C₉	—	3	1	no	—
21	C₃×C₄	—	3	3	no	—
22	C₃×C₄	—	3	1	no	—
23	C₃²	—	12	3	no	—
24	C₃²	C₃×SL(2,𝔽₃)	1	1	yes	characteristic
25	C₉	—	3	1	no	—
26	Q₈	#732	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃	—	3	1	no	—
28	C₂×C₃	—	36	3	no	—
29	C₂×C₃	C₂²⋊H(3,𝔽₃)	1	1	yes	characteristic
30	C₄	—	3	1	no	—
31	C₃	—	3	1	no	—
32	C₃	—	36	3	no	—
33	C₃	Q₈⋊H(3,𝔽₃)	1	1	yes	characteristic
34	C₂	#66358	1	1	yes	characteristic

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.