Subgroups — C₃×C₃⋊(C₃⋊C₈) #6246

Order 216.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₄	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₃⋊C₈)	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₃⋊C₈	—	3	4	no	maximal
4	C₂×C₃³	C₄	1	1	yes	characteristic
5	C₃²×C₄	—	2	4	no	—
6	C₃²×C₄	D₃	1	4	yes	—
7	C₃²×C₄	C₂×C₃	1	1	yes	characteristic
8	C₃³	C₈	1	1	yes	characteristic, complemented, Sylow
9	C₃×C₈	—	9	1	no	—
10	C₃⋊C₈	—	3	4	no	—
11	C₂×C₃²	—	2	4	no	—
12	C₂×C₃²	Dic₃	1	4	yes	—
13	C₂×C₃²	C₃×C₄	1	1	yes	characteristic
14	C₃×C₄	—	2	4	no	—
15	C₃×C₄	C₃×D₃	1	4	yes	—
16	C₃×C₄	C₃⋊D₃	1	1	yes	characteristic
17	C₃²	—	2	4	no	—
18	C₃²	C₃⋊C₈	1	4	yes	complemented
19	C₃²	C₃×C₈	1	1	yes	characteristic, complemented
20	C₈	—	9	1	no	Sylow
21	C₂×C₃	—	2	4	no	—
22	C₂×C₃	C₃×Dic₃	1	4	yes	—
23	C₂×C₃	C₃⋊Dic₃	1	1	yes	characteristic
24	C₄	C₃×C₃⋊D₃	1	1	yes	characteristic
25	C₃	—	2	4	no	—
26	C₃	C₃×C₃⋊C₈	1	4	yes	complemented
27	C₃	C₃⋊(C₃⋊C₈)	1	1	yes	characteristic, direct product factor
28	C₂	C₃×C₃⋊Dic₃	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.