Subgroups — #13049161

Order 1296.

1908 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⁴×Q₈	C₂	1	1	yes	maximal, characteristic
2	#10620175	C₂	1	1	yes	maximal, characteristic
3	C₃⋊(C₃⋊(C₃⋊(C₃⋊C₈)))	C₂	1	1	yes	maximal, characteristic
4	#88863	—	3	40	no	maximal
5	C₃⁴×C₄	—	2	1	no	—
6	C₃⁴×C₄	C₂²	1	1	yes	characteristic
7	C₃⋊(C₃⋊(C₃⋊Dic₃))	—	2	1	no	—
8	C₃³×Q₈	D₃	1	40	yes	—
9	#6308	—	3	40	no	—
10	C₃⋊(C₃⋊(C₃⋊C₈))	—	3	40	no	—
11	C₂×C₃⁴	D₄	1	1	yes	characteristic
12	#3756	—	9	130	no	—
13	C₃³×C₄	—	2	40	no	—
14	C₃³×C₄	C₂×D₃	1	40	yes	—
15	C₃⋊(C₃⋊Dic₃)	—	6	40	no	—
16	C₃⁴	Q₁₆	1	1	yes	characteristic, complemented, Sylow
17	C₃²×Q₈	C₃⋊D₃	1	130	yes	—
18	#634	—	9	130	no	—
19	C₃⋊(C₃⋊C₈)	—	9	130	no	—
20	C₂×C₃³	#67	1	40	yes	—
21	#216	—	27	40	no	—
22	C₃²×C₄	—	2	130	no	—
23	C₃²×C₄	C₂×C₃⋊D₃	1	130	yes	—
24	C₃⋊Dic₃	—	18	130	no	—
25	C₃³	#216	1	40	yes	complemented
26	C₃×Q₈	C₃⋊(C₃⋊D₃)	1	40	yes	—
27	Dic₆	—	27	40	no	—
28	C₃⋊C₈	—	27	40	no	—
29	C₂×C₃²	#638	1	130	yes	—
30	Q₁₆	—	81	1	no	Sylow
31	C₃×C₄	—	2	40	no	—
32	C₃×C₄	C₂×C₃⋊(C₃⋊D₃)	1	40	yes	—
33	Dic₃	—	54	40	no	—
34	C₃²	#3756	1	130	yes	complemented
35	Q₈	—	81	1	no	—
36	Q₈	C₃⋊(C₃⋊(C₃⋊D₃))	1	1	yes	characteristic
37	C₈	—	81	1	no	—
38	C₂×C₃	#6312	1	40	yes	—
39	C₄	—	2	1	no	—
40	C₄	—	162	1	no	—
41	C₄	C₂×C₃⋊(C₃⋊(C₃⋊D₃))	1	1	yes	characteristic
42	C₃	#88863	1	40	yes	complemented
43	C₂	#10620179	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.