Subgroups — #63551

Order 288.

57 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3746	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₁₂	C₂	1	1	yes	maximal, characteristic
3	C₃×C₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	#829	—	3	1	no	maximal
5	Dic₂₄	—	3	1	no	maximal
6	#634	—	2	1	no	—
7	C₃×Dic₆	—	2	1	no	—
8	C₃²×C₈	C₂²	1	1	yes	characteristic
9	C₃×Q₁₆	—	3	1	no	—
10	Dic₁₂	—	3	1	no	—
11	Dic₁₂	—	3	1	no	—
12	Dic₁₂	—	6	1	no	—
13	Dic₁₂	D₃	1	1	yes	characteristic
14	C₃×C₁₆	—	3	1	no	—
15	C₃⋊C₁₆	D₃	1	1	yes	characteristic
16	C₃²×C₄	D₄	1	1	yes	characteristic
17	C₃⋊Dic₃	—	4	1	no	—
18	C₃×Dic₃	—	4	1	no	—
19	Q₃₂	—	9	1	no	Sylow
20	C₃×Q₈	—	6	1	no	—
21	Dic₆	—	2	1	no	—
22	Dic₆	—	6	2	no	—
23	Dic₆	—	6	1	no	—
24	Dic₆	—	6	1	no	—
25	C₃×C₈	—	2	1	no	—
26	C₃×C₈	C₂×D₃	1	1	yes	characteristic
27	C₃×C₈	C₂×D₃	1	1	yes	characteristic
28	C₂×C₃²	D₈	1	1	yes	characteristic
29	Q₁₆	—	3	1	no	—
30	Q₁₆	—	9	1	no	—
31	C₁₆	—	3	1	no	—
32	C₃×C₄	—	2	1	no	—
33	C₃×C₄	—	12	1	no	—
34	C₃×C₄	D₁₂	1	1	yes	characteristic
35	C₃×C₄	#67	1	1	yes	characteristic
36	Dic₃	—	4	1	no	—
37	Dic₃	—	12	2	no	—
38	Dic₃	—	12	1	no	—
39	Dic₃	—	12	1	no	—
40	C₃²	Q₃₂	1	1	yes	characteristic, complemented, Sylow
41	Q₈	—	6	1	no	—
42	Q₈	—	18	1	no	—
43	C₈	D₃²	1	1	yes	characteristic
44	C₂×C₃	—	2	1	no	—
45	C₂×C₃	D₂₄	1	1	yes	characteristic
46	C₂×C₃	#213	1	1	yes	characteristic
47	C₄	—	12	1	no	—
48	C₄	—	36	1	no	—
49	C₄	#626	1	1	yes	characteristic
50	C₃	—	2	1	no	—
51	C₃	Dic₂₄	1	1	yes	characteristic, complemented
52	C₃	#829	1	1	yes	characteristic, complemented
53	C₂	#3714	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.