Subgroups — C₃⁴×#4296 #28357064

Order 13851.

10232 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×#4296	C₃	1	120	yes	maximal, direct product factor
2	C₃⁴×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₃²×#4296	C₃²	1	1170	yes	direct product factor
4	C₃³×C₁₉⋊C₃	C₉	1	80	yes	complemented
5	C₃³×C₁₉⋊C₃	C₃²	1	40	yes	—
6	C₃⁴×C₁₉	C₉	1	1	yes	characteristic, complemented
7	C₃⁴×C₉	—	19	1	no	maximal, Sylow
8	C₃³×C₁₉	C₃×C₉	1	40	yes	complemented
9	C₃²×C₁₉⋊C₃	C₃×C₉	1	1040	yes	complemented
10	C₃²×C₁₉⋊C₃	C₃³	1	130	yes	—
11	C₃×#4296	C₃³	1	1080	yes	direct product factor
12	C₃⁵	—	19	1	no	—
13	C₃³×C₉	—	19	120	no	—
14	C₃²×C₁₉	C₃²×C₉	1	130	yes	complemented
15	C₃×C₁₉⋊C₃	C₃²×C₉	1	1040	yes	complemented
16	C₃×C₁₉⋊C₃	C₃⁴	1	40	yes	—
17	#4296	C₃⁴	1	81	yes	direct product factor
18	C₃⁴	—	19	40	no	—
19	C₃⁴	—	19	80	no	—
20	C₃⁴	#4296	1	1	yes	characteristic, direct product factor
21	C₃²×C₉	—	19	1170	no	—
22	C₃×C₁₉	C₃³×C₉	1	40	yes	complemented
23	C₁₉⋊C₃	C₃³×C₉	1	80	yes	complemented
24	C₁₉⋊C₃	C₃⁵	1	1	yes	characteristic
25	C₃³	—	19	1040	no	—
26	C₃³	—	19	130	no	—
27	C₃³	C₃×#4296	1	40	yes	direct product factor
28	C₃×C₉	—	19	1080	no	—
29	C₁₉	C₃⁴×C₉	1	1	yes	characteristic, complemented, Sylow
30	C₃²	—	19	40	no	—
31	C₃²	—	19	1040	no	—
32	C₃²	C₃²×#4296	1	130	yes	direct product factor
33	C₉	—	19	81	no	—
34	C₃	—	19	1	no	—
35	C₃	—	19	80	no	—
36	C₃	C₃³×#4296	1	40	yes	direct product factor

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.