Subgroups — C₃×C₂²⋊#92788 #20258979

Order 6084.

224 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²⋊#92788	C₃	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₁₃²	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×#92788	—	4	1	no	maximal, Hall
4	C₂×C₃×C₁₃²	—	3	1	no	—
5	C₂²×C₁₃²	C₃²	1	1	yes	characteristic, complemented, Hall
6	C₃×C₁₃²	A₄	1	1	yes	characteristic, complemented
7	#92788	—	4	3	no	—
8	C₃×C₂²⋊(C₁₃⋊C₃)	—	13	14	no	maximal
9	C₂×C₁₃²	—	3	1	no	—
10	C₁₃²	C₃×A₄	1	1	yes	characteristic, complemented, Sylow
11	C₂²×C₃×C₁₃	C₁₃⋊C₃	1	14	yes	complemented
12	C₂²⋊(C₁₃⋊C₃)	—	13	42	no	—
13	C₃×C₁₃⋊C₃	—	52	14	no	—
14	C₂×C₃×C₁₃	—	3	14	no	—
15	C₂²×C₁₃	C₃×C₁₃⋊C₃	1	14	yes	complemented
16	C₃×C₁₃	C₂²⋊(C₁₃⋊C₃)	1	14	yes	complemented
17	C₁₃⋊C₃	—	52	42	no	—
18	C₃×A₄	—	169	1	no	Hall
19	C₂×C₁₃	—	3	14	no	—
20	C₁₃	C₃×C₂²⋊(C₁₃⋊C₃)	1	14	yes	complemented
21	C₂²×C₃	#92788	1	1	yes	characteristic, complemented
22	A₄	—	169	3	no	—
23	C₃²	—	676	1	no	Sylow
24	C₂×C₃	—	3	1	no	—
25	C₂²	C₃×#92788	1	1	yes	characteristic, complemented, Sylow
26	C₃	—	676	3	no	—
27	C₃	C₂²⋊#92788	1	1	yes	characteristic, direct product factor
28	C₂	—	3	1	no	—

Splittings G = N ⋊ H with N normal; H ≅ G/N.