Subgroups — 3₋¹⁺²⋊C₁₆ #88384

Order 432.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic
2	C₃×C₃⋊C₁₆	—	3	1	no	maximal
3	C₉⋊C₁₆	C₃	1	1	yes	maximal, characteristic, complemented
4	C₄×3₋¹⁺²	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	C₂×3₋¹⁺²	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	3₋¹⁺²	C₁₆	1	1	yes	characteristic, complemented, Sylow
15	C₃×C₈	—	6	1	no	—
16	C₃×C₈	C₃×D₃	1	1	yes	characteristic
17	C₂×C₃²	C₃⋊C₈	1	1	yes	characteristic
18	C₂×C₉	—	2	1	no	—
19	C₂×C₉	C₃×C₈	1	1	yes	characteristic
20	C₁₆	—	9	1	no	Sylow
21	C₃×C₄	—	6	1	no	—
22	C₃×C₄	C₃×Dic₃	1	1	yes	characteristic
23	C₃²	C₃⋊C₁₆	1	1	yes	characteristic
24	C₉	—	2	1	no	—
25	C₉	C₃×C₁₆	1	1	yes	characteristic, complemented
26	C₈	AGL(1,ℤ/9)	1	1	yes	characteristic
27	C₂×C₃	—	6	1	no	—
28	C₂×C₃	C₃×C₃⋊C₈	1	1	yes	characteristic
29	C₄	3₋¹⁺²⋊C₄	1	1	yes	characteristic
30	C₃	—	6	1	no	—
31	C₃	C₃×C₃⋊C₁₆	1	1	yes	characteristic
32	C₂	3₋¹⁺²⋊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.