Subgroups — H(3,𝔽₃)×C₃₃₁⋊C₃ #40999784

Order 26811.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₃₃₁⋊C₃	C₃	1	4	yes	maximal, complemented
2	C₃²⋊(C₃₃₁⋊C₃)	C₃	1	8	yes	maximal, complemented
3	H(3,𝔽₃)×C₃₃₁	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃²×C₃₃₁	C₃²	1	4	yes	complemented
5	C₃×C₃₃₁⋊C₃	—	3	12	no	—
6	C₃×C₃₃₁⋊C₃	C₃²	1	1	yes	characteristic
7	C₃×C₃₃₁⋊C₃	C₃²	1	8	yes	complemented
8	C₃×C₃₃₁	—	3	4	no	—
9	C₃×C₃₃₁	C₃³	1	1	yes	characteristic
10	C₃₃₁⋊C₃	—	3	8	no	—
11	C₃₃₁⋊C₃	H(3,𝔽₃)	1	3	yes	direct product factor
12	C₃₃₁	C₃×H(3,𝔽₃)	1	1	yes	characteristic, complemented, Sylow
13	C₃×H(3,𝔽₃)	—	331	1	no	maximal, Sylow
14	C₃³	—	331	4	no	—
15	H(3,𝔽₃)	—	331	8	no	—
16	H(3,𝔽₃)	C₃₃₁⋊C₃	1	1	yes	characteristic, direct product factor
17	C₃²	—	331	1	no	—
18	C₃²	—	331	8	no	—
19	C₃²	—	993	12	no	—
20	C₃²	C₃×C₃₃₁⋊C₃	1	4	yes	complemented
21	C₃	—	3	4	no	—
22	C₃	—	331	3	no	—
23	C₃	—	993	8	no	—
24	C₃	C₃²×C₃₃₁⋊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.