Subgroups — 3₋¹⁺²×C₃₂ #11720105

Order 864.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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