Subgroups — C₉×Dic₆ #6207

Order 216.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₉	C₂	1	1	yes	maximal, characteristic
2	C₉×Dic₃	C₂	1	2	yes	maximal
3	C₃×Dic₆	C₃	1	1	yes	maximal, characteristic
4	Q₈×C₉	—	3	1	no	maximal
5	C₂×C₃×C₉	C₂²	1	1	yes	characteristic
6	C₃²×C₄	C₂×C₃	1	1	yes	characteristic
7	C₃×Dic₃	C₂×C₃	1	2	yes	—
8	C₄×C₉	—	2	1	no	—
9	C₄×C₉	—	3	2	no	—
10	C₄×C₉	D₃	1	1	yes	characteristic
11	C₃×C₉	Q₈	1	1	yes	characteristic, complemented, Sylow
12	C₃×Q₈	—	3	1	no	—
13	Dic₆	C₉	1	1	yes	characteristic, direct product factor
14	C₂×C₃²	C₂²×C₃	1	1	yes	characteristic
15	C₂×C₉	—	2	1	no	—
16	C₂×C₉	C₂×D₃	1	1	yes	characteristic
17	C₃×C₄	—	2	1	no	—
18	C₃×C₄	—	3	2	no	—
19	C₃×C₄	C₂×C₉	1	1	yes	characteristic
20	C₃×C₄	C₃×D₃	1	1	yes	characteristic
21	Dic₃	C₂×C₉	1	2	yes	—
22	C₃²	C₃×Q₈	1	1	yes	characteristic
23	C₉	—	2	1	no	—
24	C₉	Dic₆	1	1	yes	characteristic, direct product factor
25	Q₈	—	3	1	no	Sylow
26	C₂×C₃	—	2	1	no	—
27	C₂×C₃	C₂²×C₉	1	1	yes	characteristic
28	C₂×C₃	C₂×C₃×D₃	1	1	yes	characteristic
29	C₄	—	3	2	no	—
30	C₄	D₃×C₉	1	1	yes	characteristic
31	C₃	—	2	1	no	—
32	C₃	Q₈×C₉	1	1	yes	characteristic, complemented
33	C₃	C₃×Dic₆	1	1	yes	characteristic
34	C₂	C₂×D₃×C₉	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.