Subgroups — C₃×C₂²⋊#92789 #20258977

Order 6084.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²⋊#92789	C₃	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₁₃²	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×#92789	—	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	#92789	—	4	3	no	—
8	C₃×C₂²⋊(C₁₃⋊C₃)	—	13	2	no	maximal
9	C₂×C₁₃²	—	3	1	no	—
10	C₁₃²	C₃×A₄	1	1	yes	characteristic, complemented, Sylow
11	C₂²×C₃×C₁₃	—	3	4	no	—
12	C₂²×C₃×C₁₃	C₁₃⋊C₃	1	2	yes	complemented
13	C₂²⋊(C₁₃⋊C₃)	—	13	6	no	—
14	C₃×C₁₃⋊C₃	—	52	2	no	—
15	C₂×C₃×C₁₃	—	3	12	no	—
16	C₂×C₃×C₁₃	—	3	2	no	—
17	C₂²×C₁₃	—	3	4	no	—
18	C₂²×C₁₃	C₃×C₁₃⋊C₃	1	2	yes	complemented
19	C₃×C₁₃	—	3	4	no	—
20	C₃×C₁₃	C₂²⋊(C₁₃⋊C₃)	1	2	yes	complemented
21	C₁₃⋊C₃	—	52	6	no	—
22	C₃×A₄	—	169	1	no	Hall
23	C₂×C₁₃	—	3	12	no	—
24	C₂×C₁₃	—	3	2	no	—
25	C₁₃	—	3	4	no	—
26	C₁₃	C₃×C₂²⋊(C₁₃⋊C₃)	1	2	yes	complemented
27	C₂²×C₃	#92789	1	1	yes	characteristic, complemented
28	A₄	—	169	3	no	—
29	C₃²	—	676	1	no	Sylow
30	C₂×C₃	—	3	1	no	—
31	C₂²	C₃×#92789	1	1	yes	characteristic, complemented, Sylow
32	C₃	—	676	3	no	—
33	C₃	C₂²⋊#92789	1	1	yes	characteristic, direct product factor
34	C₂	—	3	1	no	—

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