Subgroups — #88852

Order 432.

308 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊(C₃⋊(C₃⋊D₃))	C₂	1	2	yes	maximal, complemented
2	C₃³×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#3745	—	3	13	no	maximal
4	C₂×C₃⋊(C₃⋊D₃)	—	2	2	no	—
5	C₃³×C₄	C₂²	1	1	yes	characteristic
6	C₄⋊(C₃⋊D₃)	—	3	26	no	—
7	C₃²×C₈	D₃	1	13	yes	complemented
8	C₂×C₃³	D₄	1	1	yes	characteristic
9	C₃⋊(C₃⋊D₃)	—	4	2	no	—
10	D₂₄	—	9	13	no	—
11	C₂×C₃⋊D₃	—	6	26	no	—
12	C₃²×C₄	C₂×D₃	1	13	yes	—
13	C₃³	D₈	1	1	yes	characteristic, complemented, Sylow
14	D₁₂	—	9	26	no	—
15	C₃×C₈	C₃⋊D₃	1	13	yes	complemented
16	C₂×C₃²	D₁₂	1	13	yes	—
17	C₃⋊D₃	—	12	26	no	—
18	D₈	—	27	1	no	Sylow
19	C₂×D₃	—	18	26	no	—
20	C₃×C₄	C₂×C₃⋊D₃	1	13	yes	—
21	C₃²	D₂₄	1	13	yes	complemented
22	D₄	—	27	2	no	—
23	C₈	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
24	C₂×C₃	C₄⋊(C₃⋊D₃)	1	13	yes	—
25	D₃	—	36	26	no	—
26	C₂²	—	54	2	no	—
27	C₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
28	C₃	#3745	1	13	yes	complemented
29	C₂	—	108	2	no	—
30	C₂	C₄⋊(C₃⋊(C₃⋊D₃))	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.