Subgroups — 3₋¹⁺²⋊C₈ #6178

Order 216.

27 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	C₃×C₃⋊C₈	—	3	1	no	maximal
3	C₉⋊C₈	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×3₋¹⁺²	C₄	1	1	yes	characteristic
5	C₃²×C₄	D₃	1	1	yes	characteristic
6	C₄×C₉	—	2	1	no	—
7	C₄×C₉	C₂×C₃	1	1	yes	characteristic
8	3₋¹⁺²	C₈	1	1	yes	characteristic, complemented, Sylow
9	C₃×C₈	—	9	1	no	—
10	C₃⋊C₈	—	3	1	no	—
11	C₂×C₃²	Dic₃	1	1	yes	characteristic
12	C₂×C₉	—	2	1	no	—
13	C₂×C₉	C₃×C₄	1	1	yes	characteristic
14	C₃×C₄	—	3	1	no	—
15	C₃×C₄	C₃×D₃	1	1	yes	characteristic
16	C₃²	C₃⋊C₈	1	1	yes	characteristic
17	C₉	—	2	1	no	—
18	C₉	C₃×C₈	1	1	yes	characteristic, complemented
19	C₈	—	9	1	no	Sylow
20	C₂×C₃	—	3	1	no	—
21	C₂×C₃	C₃×Dic₃	1	1	yes	characteristic
22	C₄	AGL(1,ℤ/9)	1	1	yes	characteristic
23	C₃	—	3	1	no	—
24	C₃	C₃×C₃⋊C₈	1	1	yes	characteristic
25	C₂	3₋¹⁺²⋊C₄	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.