Subgroups — C₃×C₃⋊(C₃⋊C₁₆) #88583

Order 432.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₈	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₃⋊C₁₆)	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₃⋊C₁₆	—	3	4	no	maximal
4	C₃³×C₄	C₄	1	1	yes	characteristic
5	C₃²×C₈	—	2	4	no	—
6	C₃²×C₈	D₃	1	4	yes	—
7	C₃²×C₈	C₂×C₃	1	1	yes	characteristic
8	C₂×C₃³	C₈	1	1	yes	characteristic
9	C₃×C₁₆	—	9	1	no	—
10	C₃⋊C₁₆	—	3	4	no	—
11	C₃²×C₄	—	2	4	no	—
12	C₃²×C₄	Dic₃	1	4	yes	—
13	C₃²×C₄	C₃×C₄	1	1	yes	characteristic
14	C₃³	C₁₆	1	1	yes	characteristic, complemented, Sylow
15	C₃×C₈	—	2	4	no	—
16	C₃×C₈	C₃×D₃	1	4	yes	—
17	C₃×C₈	C₃⋊D₃	1	1	yes	characteristic
18	C₂×C₃²	—	2	4	no	—
19	C₂×C₃²	C₃⋊C₈	1	4	yes	—
20	C₂×C₃²	C₃×C₈	1	1	yes	characteristic
21	C₁₆	—	9	1	no	Sylow
22	C₃×C₄	—	2	4	no	—
23	C₃×C₄	C₃×Dic₃	1	4	yes	—
24	C₃×C₄	C₃⋊Dic₃	1	1	yes	characteristic
25	C₃²	—	2	4	no	—
26	C₃²	C₃⋊C₁₆	1	4	yes	complemented
27	C₃²	C₃×C₁₆	1	1	yes	characteristic, complemented
28	C₈	C₃×C₃⋊D₃	1	1	yes	characteristic
29	C₂×C₃	—	2	4	no	—
30	C₂×C₃	C₃×C₃⋊C₈	1	4	yes	—
31	C₂×C₃	C₃⋊(C₃⋊C₈)	1	1	yes	characteristic
32	C₄	C₃×C₃⋊Dic₃	1	1	yes	characteristic
33	C₃	—	2	4	no	—
34	C₃	C₃×C₃⋊C₁₆	1	4	yes	complemented
35	C₃	C₃⋊(C₃⋊C₁₆)	1	1	yes	characteristic, direct product factor
36	C₂	C₃×C₃⋊(C₃⋊C₈)	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.