Subgroups — #11722199

Order 864.

336 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	#88853	C₂	1	1	yes	maximal, characteristic
3	C₃⋊(C₃⋊(C₃⋊C₁₆))	C₂	1	1	yes	maximal, characteristic
4	#63656	—	3	13	no	maximal
5	C₃³×Q₈	—	2	1	no	—
6	#6308	—	2	1	no	—
7	C₃³×C₈	C₂²	1	1	yes	characteristic
8	C₃²×Q₁₆	D₃	1	13	yes	—
9	#3746	—	3	13	no	—
10	C₃⋊(C₃⋊C₁₆)	—	3	13	no	—
11	C₃³×C₄	—	4	1	no	—
12	C₃³×C₄	D₄	1	1	yes	characteristic
13	C₃⋊(C₃⋊Dic₃)	—	4	1	no	—
14	#829	—	9	13	no	—
15	C₃²×Q₈	—	2	13	no	—
16	#634	—	6	13	no	—
17	C₃²×C₈	C₂×D₃	1	13	yes	—
18	C₂×C₃³	D₈	1	1	yes	characteristic
19	C₃×Q₁₆	C₃⋊D₃	1	13	yes	—
20	Dic₁₂	—	9	13	no	—
21	C₃⋊C₁₆	—	9	13	no	—
22	C₃²×C₄	—	4	13	no	—
23	C₃²×C₄	#67	1	13	yes	—
24	C₃⋊Dic₃	—	12	13	no	—
25	Q₃₂	—	27	1	no	Sylow
26	C₃³	Q₃₂	1	1	yes	characteristic, complemented, Sylow
27	C₃×Q₈	—	2	13	no	—
28	Dic₆	—	18	13	no	—
29	C₃×C₈	C₂×C₃⋊D₃	1	13	yes	—
30	C₂×C₃²	#213	1	13	yes	—
31	Q₁₆	—	27	1	no	—
32	Q₁₆	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
33	C₁₆	—	27	1	no	—
34	C₃×C₄	—	4	13	no	—
35	C₃×C₄	#638	1	13	yes	—
36	Dic₃	—	36	13	no	—
37	C₃²	#829	1	13	yes	complemented
38	Q₈	—	2	1	no	—
39	Q₈	—	54	1	no	—
40	C₈	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
41	C₂×C₃	#3753	1	13	yes	—
42	C₄	—	4	1	no	—
43	C₄	—	108	1	no	—
44	C₄	#6312	1	1	yes	characteristic
45	C₃	#63656	1	13	yes	complemented
46	C₂	#88860	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.