Subgroups — #64083

Order 288.

324 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊(C₃⋊D₃)	C₂	1	6	yes	maximal, complemented
2	C₃²×C₄²	C₂	1	1	yes	maximal, characteristic, complemented
3	#874	—	3	4	no	maximal
4	C₂²×C₃⋊D₃	C₂²	1	4	yes	—
5	C₂×C₃²×C₄	C₂²	1	3	yes	—
6	C₄⋊(C₃⋊D₃)	—	2	12	no	—
7	C₂×D₁₂	—	3	24	no	—
8	C₃×C₄²	D₃	1	4	yes	complemented
9	C₂²×C₃²	C₂³	1	1	yes	characteristic
10	C₂×C₃⋊D₃	—	2	12	no	—
11	C₃²×C₄	D₄	1	6	yes	complemented
12	#127	—	9	1	no	Sylow
13	C₂²×D₃	—	3	16	no	—
14	C₂×C₃×C₄	C₂×D₃	1	12	yes	—
15	D₁₂	—	6	48	no	—
16	C₂×C₃²	C₂×D₄	1	3	yes	—
17	C₃⋊D₃	—	4	4	no	—
18	C₂×D₄	—	9	6	no	—
19	C₄²	C₃⋊D₃	1	1	yes	characteristic, complemented
20	C₂²×C₃	C₂²×D₃	1	4	yes	—
21	C₂×D₃	—	6	48	no	—
22	C₃×C₄	D₁₂	1	24	yes	complemented
23	C₃²	#127	1	1	yes	characteristic, complemented, Sylow
24	C₂³	—	9	4	no	—
25	D₄	—	18	12	no	—
26	C₂×C₄	C₂×C₃⋊D₃	1	3	yes	—
27	C₂×C₃	C₂×D₁₂	1	12	yes	—
28	D₃	—	12	16	no	—
29	C₂²	—	18	12	no	—
30	C₂²	C₂²×C₃⋊D₃	1	1	yes	characteristic
31	C₄	C₄⋊(C₃⋊D₃)	1	6	yes	complemented
32	C₃	#874	1	4	yes	complemented
33	C₂	—	36	4	no	—
34	C₂	C₂×C₄⋊(C₃⋊D₃)	1	3	yes	—

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.