Subgroups — #10619913

Order 648.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
2	#6204	C₃	1	8	yes	maximal, complemented
3	C₃×Q₈⋊C₉	C₃	1	4	yes	maximal, complemented
4	C₂×#737	—	4	1	no	maximal
5	C₄×H(3,𝔽₃)	—	3	1	no	—
6	#737	—	4	1	no	Sylow
7	C₃²×Q₈	C₃²	1	4	yes	—
8	Q₈⋊C₉	C₃²	1	1	yes	characteristic
9	Q₈⋊C₉	C₃²	1	8	yes	—
10	C₂×3₋¹⁺²	—	4	8	no	—
11	C₂×H(3,𝔽₃)	A₄	1	1	yes	characteristic
12	C₂×C₃×C₉	—	4	4	no	—
13	C₃²×C₄	—	3	4	no	—
14	3₋¹⁺²	—	4	8	no	—
15	H(3,𝔽₃)	SL(2,𝔽₃)	1	1	yes	characteristic
16	C₃×C₉	—	4	4	no	—
17	C₃×Q₈	—	3	4	no	—
18	C₃×Q₈	C₃³	1	1	yes	characteristic
19	C₂×C₃²	C₃×A₄	1	4	yes	—
20	C₂×C₉	—	4	1	no	—
21	C₂×C₉	—	4	8	no	—
22	C₃×C₄	—	3	1	no	—
23	C₃×C₄	—	9	4	no	—
24	C₃²	C₃×SL(2,𝔽₃)	1	4	yes	—
25	C₉	—	4	1	no	—
26	C₉	—	4	8	no	—
27	Q₈	#737	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	3	4	no	—
29	C₂×C₃	C₃²×A₄	1	1	yes	characteristic
30	C₄	—	3	1	no	—
31	C₃	—	3	4	no	—
32	C₃	C₃²×SL(2,𝔽₃)	1	1	yes	characteristic
33	C₂	#66437	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.