Subgroups — 3₋¹⁺²⋊Q₈ #6215

Order 216.

39 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	3₋¹⁺²⋊C₄	C₂	1	2	yes	maximal
3	C₃×Dic₆	—	3	1	no	maximal
4	Dic₁₈	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂×3₋¹⁺²	C₂²	1	1	yes	characteristic
6	C₃²×C₄	D₃	1	1	yes	characteristic
7	C₃×Dic₃	—	3	2	no	—
8	C₄×C₉	—	2	1	no	—
9	C₄×C₉	C₂×C₃	1	1	yes	characteristic
10	Dic₉	C₂×C₃	1	2	yes	—
11	3₋¹⁺²	Q₈	1	1	yes	characteristic, complemented, Sylow
12	C₃×Q₈	—	9	1	no	—
13	Dic₆	—	3	1	no	—
14	C₂×C₃²	C₂×D₃	1	1	yes	characteristic
15	C₂×C₉	—	2	1	no	—
16	C₂×C₉	C₂²×C₃	1	1	yes	characteristic
17	C₃×C₄	—	3	1	no	—
18	C₃×C₄	—	9	2	no	—
19	C₃×C₄	C₃×D₃	1	1	yes	characteristic
20	Dic₃	—	3	2	no	—
21	C₃²	Dic₆	1	1	yes	characteristic
22	C₉	—	2	1	no	—
23	C₉	C₃×Q₈	1	1	yes	characteristic, complemented
24	Q₈	—	9	1	no	Sylow
25	C₂×C₃	—	3	1	no	—
26	C₂×C₃	C₂×C₃×D₃	1	1	yes	characteristic
27	C₄	—	9	2	no	—
28	C₄	AGL(1,ℤ/9)	1	1	yes	characteristic
29	C₃	—	3	1	no	—
30	C₃	C₃×Dic₆	1	1	yes	characteristic
31	C₂	C₂×AGL(1,ℤ/9)	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.