Subgroups — (C₃⋊(C₃⋊C₈))⋊C₃ #6177

Order 216.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×H(3,𝔽₃)	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₃⋊C₈)	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×C₃⋊C₈	—	3	1	no	maximal
4	C₂×H(3,𝔽₃)	C₄	1	1	yes	characteristic
5	C₃²×C₄	—	2	1	no	—
6	C₃²×C₄	D₃	1	1	yes	characteristic
7	C₃²×C₄	C₂×C₃	1	1	yes	characteristic
8	H(3,𝔽₃)	C₈	1	1	yes	characteristic, complemented, Sylow
9	C₃×C₈	—	9	1	no	—
10	C₃⋊C₈	—	3	1	no	—
11	C₃⋊C₈	—	9	1	no	—
12	C₂×C₃²	—	2	1	no	—
13	C₂×C₃²	Dic₃	1	1	yes	characteristic
14	C₂×C₃²	C₃×C₄	1	1	yes	characteristic
15	C₃×C₄	—	3	1	no	—
16	C₃×C₄	—	3	1	no	—
17	C₃×C₄	—	6	1	no	—
18	C₃×C₄	C₃×D₃	1	1	yes	characteristic
19	C₃²	—	2	1	no	—
20	C₃²	C₃⋊C₈	1	1	yes	characteristic, complemented
21	C₃²	C₃×C₈	1	1	yes	characteristic, complemented
22	C₈	—	9	1	no	Sylow
23	C₂×C₃	—	3	1	no	—
24	C₂×C₃	—	3	1	no	—
25	C₂×C₃	—	6	1	no	—
26	C₂×C₃	C₃×Dic₃	1	1	yes	characteristic
27	C₄	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
28	C₃	—	3	1	no	—
29	C₃	—	3	1	no	—
30	C₃	—	6	1	no	—
31	C₃	C₃×C₃⋊C₈	1	1	yes	characteristic
32	C₂	(C₃⋊Dic₃)⋊C₃	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.