Subgroups — #2258⋊C₃ #68044

Order 384.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#504⋊C₃	C₂	1	1	yes	maximal, characteristic
2	#2258	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
3	#131⋊C₃	C₄	1	1	yes	characteristic
4	C₃×C₃₂	—	4	1	no	maximal
5	#504	C₂×C₃	1	1	yes	characteristic
6	M₆₄	—	3	1	no	—
7	C₂×C₃₂	—	3	1	no	—
8	#41⋊C₃	C₈	1	1	yes	characteristic
9	C₃×C₁₆	—	4	1	no	—
10	#131	C₃×C₄	1	1	yes	characteristic
11	M₃₂	—	3	1	no	—
12	C₂×C₁₆	—	3	1	no	—
13	C₃₂	—	3	1	no	—
14	C₃₂	A₄	1	1	yes	characteristic
15	SL(2,𝔽₃)	C₁₆	1	1	yes	characteristic
16	C₃×C₈	—	4	1	no	—
17	#41	C₃×C₈	1	1	yes	characteristic
18	M₁₆	—	3	1	no	—
19	C₂×C₈	—	3	1	no	—
20	C₁₆	—	3	1	no	—
21	C₁₆	C₂×A₄	1	1	yes	characteristic
22	C₃×C₄	—	4	1	no	—
23	Q₈	C₃×C₁₆	1	1	yes	characteristic
24	D₄	—	3	1	no	—
25	C₂×C₄	—	3	1	no	—
26	C₈	—	3	1	no	—
27	C₈	C₄×A₄	1	1	yes	characteristic
28	C₂×C₃	—	4	1	no	—
29	C₂²	—	3	1	no	—
30	C₄	—	3	1	no	—
31	C₄	C₈×A₄	1	1	yes	characteristic
32	C₃	—	4	1	no	Sylow
33	C₂	—	6	1	no	—
34	C₂	A₄×C₁₆	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. #2258	C₃	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.