Subgroups — C₃×C₉⋊C₁₆ #88381

Order 432.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₈×C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₃⋊C₁₆	—	3	1	no	maximal
3	C₉⋊C₁₆	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₃×C₄×C₉	C₄	1	1	yes	characteristic
5	C₃²×C₈	D₃	1	1	yes	characteristic
6	C₈×C₉	—	2	1	no	—
7	C₈×C₉	C₂×C₃	1	1	yes	characteristic
8	C₂×C₃×C₉	C₈	1	1	yes	characteristic
9	C₃×C₁₆	—	9	1	no	—
10	C₃⋊C₁₆	—	3	1	no	—
11	C₃²×C₄	Dic₃	1	1	yes	characteristic
12	C₄×C₉	—	2	1	no	—
13	C₄×C₉	C₃×C₄	1	1	yes	characteristic
14	C₃×C₉	C₁₆	1	1	yes	characteristic, complemented, Sylow
15	C₃×C₈	—	2	1	no	—
16	C₃×C₈	D₉	1	1	yes	characteristic
17	C₃×C₈	C₃×D₃	1	1	yes	characteristic
18	C₂×C₃²	C₃⋊C₈	1	1	yes	characteristic
19	C₂×C₉	—	2	1	no	—
20	C₂×C₉	C₃×C₈	1	1	yes	characteristic
21	C₁₆	—	9	1	no	Sylow
22	C₃×C₄	—	2	1	no	—
23	C₃×C₄	Dic₉	1	1	yes	characteristic
24	C₃×C₄	C₃×Dic₃	1	1	yes	characteristic
25	C₃²	C₃⋊C₁₆	1	1	yes	characteristic
26	C₉	—	2	1	no	—
27	C₉	C₃×C₁₆	1	1	yes	characteristic, complemented
28	C₈	C₃×D₉	1	1	yes	characteristic
29	C₂×C₃	—	2	1	no	—
30	C₂×C₃	C₉⋊C₈	1	1	yes	characteristic
31	C₂×C₃	C₃×C₃⋊C₈	1	1	yes	characteristic
32	C₄	C₃×Dic₉	1	1	yes	characteristic
33	C₃	—	2	1	no	—
34	C₃	C₉⋊C₁₆	1	1	yes	characteristic, direct product factor
35	C₃	C₃×C₃⋊C₁₆	1	1	yes	characteristic
36	C₂	C₃×C₉⋊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.