Subgroups — C₈×3₋¹⁺² #6183

Order 216.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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