Subgroups — #63644

Order 288.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₈	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₃⋊Dic₃)	C₂	1	2	yes	maximal
3	#817	—	3	4	no	maximal
4	C₂×C₃²×C₄	C₂²	1	1	yes	characteristic
5	C₂×C₃⋊Dic₃	—	2	2	no	—
6	C₃²×C₈	C₄	1	2	yes	complemented
7	C₂×C₃×C₈	D₃	1	4	yes	—
8	C₄⋊Dic₃	—	3	8	no	—
9	C₂²×C₃²	D₄	1	1	yes	characteristic
10	C₃²×C₄	C₂×C₄	1	1	yes	characteristic
11	C₃²×C₄	Q₈	1	1	yes	characteristic
12	C₃⋊Dic₃	—	4	2	no	—
13	#106	—	9	1	no	Sylow
14	C₂×C₃×C₄	C₂×D₃	1	4	yes	—
15	C₂×Dic₃	—	6	8	no	—
16	C₃×C₈	Dic₃	1	8	yes	complemented
17	C₂×C₃²	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₃²	SD₁₆	1	2	yes	—
19	C₂×C₈	C₃⋊D₃	1	1	yes	characteristic
20	C₄⋊C₄	—	9	2	no	—
21	C₂²×C₃	D₁₂	1	4	yes	—
22	C₃×C₄	Dic₆	1	4	yes	—
23	C₃×C₄	C₂×Dic₃	1	4	yes	—
24	Dic₃	—	12	8	no	—
25	C₃²	#106	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₄	—	18	2	no	—
27	C₂×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
28	C₈	C₃⋊Dic₃	1	2	yes	complemented
29	C₂×C₃	#204	1	8	yes	—
30	C₂×C₃	C₄⋊Dic₃	1	4	yes	—
31	C₂²	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
32	C₄	—	36	2	no	—
33	C₄	#634	1	1	yes	characteristic
34	C₄	C₂×C₃⋊Dic₃	1	1	yes	characteristic
35	C₃	#817	1	4	yes	complemented
36	C₂	#3744	1	2	yes	—
37	C₂	C₄⋊(C₃⋊Dic₃)	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.