Subgroups — C₃×C₉⋊C₈ #6175

Order 216.

30 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	C₃×C₃⋊C₈	—	3	1	no	maximal
3	C₉⋊C₈	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₂×C₃×C₉	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	C₃×C₉	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	—	2	1	no	—
15	C₃×C₄	D₉	1	1	yes	characteristic
16	C₃×C₄	C₃×D₃	1	1	yes	characteristic
17	C₃²	C₃⋊C₈	1	1	yes	characteristic
18	C₉	—	2	1	no	—
19	C₉	C₃×C₈	1	1	yes	characteristic, complemented
20	C₈	—	9	1	no	Sylow
21	C₂×C₃	—	2	1	no	—
22	C₂×C₃	Dic₉	1	1	yes	characteristic
23	C₂×C₃	C₃×Dic₃	1	1	yes	characteristic
24	C₄	C₃×D₉	1	1	yes	characteristic
25	C₃	—	2	1	no	—
26	C₃	C₉⋊C₈	1	1	yes	characteristic, direct product factor
27	C₃	C₃×C₃⋊C₈	1	1	yes	characteristic
28	C₂	C₃×Dic₉	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.