Subgroups — #11757397

Order 972.

71 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₉²	C₃	1	1	yes	maximal, characteristic, complemented
2	#66358	C₃	1	3	yes	maximal, complemented
3	#6879	—	4	1	no	maximal, Sylow
4	C₂×C₉²	—	3	1	no	—
5	C₂²×C₃×C₉	—	3	1	no	—
6	C₂²×C₃×C₉	C₃²	1	1	yes	characteristic
7	C₂²⋊H(3,𝔽₃)	—	3	3	no	—
8	#732	—	4	3	no	—
9	C₉²	A₄	1	1	yes	characteristic, complemented
10	C₂×C₃×C₉	—	3	3	no	—
11	C₂×C₃×C₉	—	3	1	no	—
12	C₂²×C₃²	H(3,𝔽₃)	1	1	yes	characteristic
13	C₃×A₄	—	9	3	no	—
14	C₂²×C₉	—	3	3	no	—
15	C₂²×C₉	—	3	1	no	—
16	H(3,𝔽₃)	—	12	3	no	—
17	C₃×C₉	—	3	1	no	—
18	C₃×C₉	C₃×A₄	1	1	yes	characteristic
19	C₂×C₃²	—	3	1	no	—
20	C₂×C₉	—	3	9	no	—
21	C₂×C₉	—	3	3	no	—
22	C₂²×C₃	—	3	1	no	—
23	C₂²×C₃	#732	1	1	yes	characteristic
24	A₄	—	27	3	no	—
25	C₃²	—	36	3	no	—
26	C₃²	C₂²⋊H(3,𝔽₃)	1	1	yes	characteristic
27	C₉	—	3	3	no	—
28	C₉	—	3	1	no	—
29	C₂×C₃	—	3	3	no	—
30	C₂×C₃	—	3	1	no	—
31	C₂²	#6879	1	1	yes	characteristic, complemented, Sylow
32	C₃	—	3	1	no	—
33	C₃	—	108	3	no	—
34	C₃	#66358	1	1	yes	characteristic
35	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.