Subgroups — #10596487

Order 576.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#64289	C₂	1	1	yes	maximal, characteristic
2	#64214	C₂	1	3	yes	maximal, complemented
3	#64213	C₂	1	3	yes	maximal, complemented
4	#3832	C₄	1	1	yes	characteristic
5	#3788	C₄	1	3	yes	—
6	#3787	C₂²	1	3	yes	—
7	#3771	C₂²	1	1	yes	characteristic
8	#3771	C₂²	1	3	yes	—
9	C₃²×Q₈	C₈	1	1	yes	characteristic
10	C₄⋊(C₃⋊D₃)	C₈	1	3	yes	—
11	C₄×C₃⋊D₃	C₂×C₄	1	3	yes	—
12	#622	C₂×C₄	1	3	yes	—
13	#622	C₂³	1	1	yes	characteristic
14	#504	—	9	1	no	maximal, Sylow
15	#239	—	12	1	no	—
16	C₂×C₃⋊D₃	C₂×C₈	1	3	yes	—
17	C₃²×C₄	C₂×C₈	1	3	yes	—
18	C₃⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
19	#131	—	9	1	no	—
20	M₃₂	—	9	3	no	—
21	C₂×C₁₆	—	9	3	no	—
22	C₃×Q₈	—	4	1	no	—
23	D₁₂	—	12	3	no	—
24	C₄×D₃	—	12	3	no	—
25	C₂×C₃²	C₂²×C₈	1	1	yes	characteristic
26	C₃⋊D₃	—	2	3	no	—
27	#41	—	9	1	no	—
28	M₁₆	—	9	3	no	—
29	C₂×C₈	—	9	3	no	—
30	C₁₆	—	9	1	no	—
31	C₁₆	—	9	3	no	—
32	C₂×D₃	—	12	3	no	—
33	C₃×C₄	—	4	3	no	—
34	Dic₃	—	12	1	no	—
35	C₃²	#504	1	1	yes	characteristic, complemented, Sylow
36	Q₈	AGL(1,𝔽₉)	1	1	yes	characteristic
37	D₄	—	9	3	no	—
38	C₂×C₄	—	9	3	no	—
39	C₈	—	9	1	no	—
40	C₈	—	9	3	no	—
41	C₂×C₃	—	4	1	no	—
42	D₃	—	24	3	no	—
43	C₂²	—	9	3	no	—
44	C₄	—	9	1	no	—
45	C₄	C₂×AGL(1,𝔽₉)	1	3	yes	—
46	C₃	—	4	1	no	—
47	C₂	—	18	3	no	—
48	C₂	C₂²×AGL(1,𝔽₉)	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.