Subgroups — #578⋊C₃ #5460

Order 192.

73 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	2₋¹⁺⁴⋊C₃	C₂	1	2	yes	maximal, complemented
2	#131⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#578	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
4	#41⋊C₃	C₂²	1	1	yes	characteristic
5	C₂×SL(2,𝔽₃)	—	2	2	no	—
6	C₃×D₈	—	4	1	no	maximal
7	2₋¹⁺⁴	C₂×C₃	1	2	yes	complemented
8	#137	—	3	2	no	—
9	#135	—	3	1	no	—
10	C₂×Q₁₆	—	3	1	no	—
11	#131	C₂×C₃	1	1	yes	characteristic, complemented
12	C₃×D₄	—	4	2	no	—
13	SL(2,𝔽₃)	D₄	1	1	yes	characteristic
14	C₃×C₈	—	4	1	no	—
15	#41	—	3	2	no	—
16	#41	—	6	2	no	—
17	#41	C₂²×C₃	1	1	yes	characteristic
18	C₂×Q₈	—	2	2	no	—
19	C₂×Q₈	—	3	2	no	—
20	Q₁₆	—	3	2	no	—
21	Q₁₆	—	3	1	no	—
22	SD₁₆	—	3	2	no	—
23	D₈	A₄	1	1	yes	characteristic
24	M₁₆	—	3	1	no	—
25	C₂×C₈	—	3	1	no	—
26	C₂²×C₃	—	8	2	no	—
27	C₃×C₄	—	4	1	no	—
28	Q₈	—	3	2	no	—
29	Q₈	—	6	2	no	—
30	Q₈	C₃×D₄	1	1	yes	characteristic
31	D₄	—	3	1	no	—
32	D₄	—	6	2	no	—
33	D₄	C₂×A₄	1	2	yes	—
34	C₂×C₄	—	3	1	no	—
35	C₂×C₄	—	6	2	no	—
36	C₂×C₄	—	6	2	no	—
37	C₈	—	3	1	no	—
38	C₈	C₂×A₄	1	1	yes	characteristic
39	C₂×C₃	—	4	1	no	—
40	C₂×C₃	—	16	2	no	—
41	C₂²	—	2	2	no	—
42	C₂²	—	3	1	no	—
43	C₄	—	3	1	no	—
44	C₄	—	6	2	no	—
45	C₄	C₂²×A₄	1	1	yes	characteristic
46	C₃	—	4	1	no	Sylow
47	C₂	—	4	2	no	—
48	C₂	—	6	1	no	—
49	C₂	D₄×A₄	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.