Subgroups — #1088⋊C₂ #6250

Order 216.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	((C₃⋊D₃)⋊C₃)⋊C₂	C₂	1	2	yes	maximal, complemented
2	#1088	C₂	1	1	yes	maximal, characteristic, complemented
3	#272	C₂²	1	1	yes	characteristic
4	(C₃⋊D₃)⋊C₃	—	2	2	no	—
5	D₃²	—	6	2	no	—
6	H(3,𝔽₃)	D₄	1	1	yes	characteristic, complemented, Sylow
7	D₁₂	—	9	1	no	maximal
8	C₃⋊D₃	—	2	2	no	—
9	C₃×D₃	—	6	2	no	—
10	C₃×D₃	—	6	2	no	—
11	C₂×D₃	—	9	2	no	—
12	C₂×D₃	—	18	2	no	—
13	C₃×C₄	—	9	1	no	—
14	C₃²	—	2	2	no	—
15	D₄	—	27	1	no	Sylow
16	C₂×C₃	—	9	1	no	—
17	C₂×C₃	—	18	2	no	—
18	D₃	—	6	2	no	—
19	D₃	—	6	2	no	—
20	D₃	—	18	2	no	—
21	C₂²	—	27	2	no	—
22	C₄	—	9	1	no	—
23	C₃	—	6	2	no	—
24	C₃	GO⁺(4,𝔽₂)	1	1	yes	characteristic
25	C₂	—	9	1	no	—
26	C₂	—	18	2	no	—

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.