Subgroups — #88861

Order 432.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×D₄	C₂	1	1	yes	maximal, characteristic
2	#6308	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊(C₃⋊(C₃⋊C₈))	C₂	1	1	yes	maximal, characteristic, complemented
4	#3754	—	3	13	no	maximal
5	C₂²×C₃³	—	2	1	no	—
6	C₃³×C₄	C₂²	1	1	yes	characteristic
7	C₃⋊(C₃⋊Dic₃)	—	2	1	no	—
8	C₃²×D₄	D₃	1	13	yes	—
9	#634	—	3	13	no	—
10	C₃⋊(C₃⋊C₈)	—	3	13	no	—
11	C₂×C₃³	—	4	1	no	—
12	C₂×C₃³	D₄	1	1	yes	characteristic
13	#214	—	9	13	no	—
14	C₂²×C₃²	—	2	13	no	—
15	C₃²×C₄	C₂×D₃	1	13	yes	—
16	C₃⋊Dic₃	—	6	13	no	—
17	C₃³	SD₁₆	1	1	yes	characteristic, complemented, Sylow
18	C₃×D₄	C₃⋊D₃	1	13	yes	—
19	Dic₆	—	9	13	no	—
20	C₃⋊C₈	—	9	13	no	—
21	C₂×C₃²	—	4	13	no	—
22	C₂×C₃²	#67	1	13	yes	—
23	SD₁₆	—	27	1	no	Sylow
24	C₂²×C₃	—	2	13	no	—
25	C₃×C₄	C₂×C₃⋊D₃	1	13	yes	—
26	Dic₃	—	18	13	no	—
27	C₃²	#214	1	13	yes	complemented
28	Q₈	—	27	1	no	—
29	D₄	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
30	C₈	—	27	1	no	—
31	C₂×C₃	—	4	13	no	—
32	C₂×C₃	#638	1	13	yes	—
33	C₂²	—	2	1	no	—
34	C₄	—	54	1	no	—
35	C₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
36	C₃	#3754	1	13	yes	complemented
37	C₂	—	4	1	no	—
38	C₂	#6312	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.