Subgroups — C₂²⋊H(3,𝔽₃) #1095

Order 108.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²	C₃	1	1	yes	maximal, characteristic, complemented
2	C₃×A₄	C₃	1	3	yes	maximal, complemented
3	H(3,𝔽₃)	—	4	1	no	maximal, Sylow
4	C₂×C₃²	—	3	1	no	—
5	C₂²×C₃	—	3	1	no	—
6	C₂²×C₃	C₃²	1	1	yes	characteristic
7	A₄	—	3	3	no	—
8	C₃²	—	4	3	no	—
9	C₃²	A₄	1	1	yes	characteristic, complemented
10	C₂×C₃	—	3	3	no	—
11	C₂×C₃	—	3	1	no	—
12	C₂²	H(3,𝔽₃)	1	1	yes	characteristic, complemented, Sylow
13	C₃	—	3	1	no	—
14	C₃	—	12	3	no	—
15	C₃	C₃×A₄	1	1	yes	characteristic
16	C₂	—	3	1	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.