Subgroups — C₃×#1425 #67985

Order 384.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₃₂	C₂	1	1	yes	maximal, characteristic
2	C₃×#368	C₂	1	2	yes	maximal
3	#1425	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂×C₃×C₁₆	C₂²	1	1	yes	characteristic
5	C₃×#108	—	2	2	no	—
6	C₃×C₃₂	C₄	1	2	yes	—
7	C₂×C₃₂	C₂×C₃	1	1	yes	characteristic
8	#368	C₂×C₃	1	2	yes	—
9	C₃×M₁₆	—	4	2	no	—
10	C₂×C₃×C₈	D₄	1	1	yes	characteristic
11	C₃×C₁₆	C₂×C₄	1	1	yes	characteristic
12	C₃×C₁₆	Q₈	1	1	yes	characteristic
13	C₂×C₁₆	C₂²×C₃	1	1	yes	characteristic
14	#108	—	2	2	no	—
15	C₃₂	C₃×C₄	1	2	yes	—
16	C₂×C₃×C₄	D₈	1	1	yes	characteristic
17	C₃×C₈	—	8	2	no	—
18	C₃×C₈	C₄⋊C₄	1	1	yes	characteristic
19	C₃×C₈	Q₁₆	1	1	yes	characteristic
20	M₁₆	—	4	2	no	—
21	C₂×C₈	C₃×D₄	1	1	yes	characteristic
22	C₁₆	C₂×C₃×C₄	1	1	yes	characteristic
23	C₁₆	C₃×Q₈	1	1	yes	characteristic
24	C₂²×C₃	Q₃₂	1	1	yes	characteristic
25	C₃×C₄	#107	1	1	yes	characteristic
26	C₃×C₄	D₁₆	1	1	yes	characteristic
27	C₂×C₄	C₃×D₈	1	1	yes	characteristic
28	C₈	—	8	2	no	—
29	C₈	C₃×C₄⋊C₄	1	1	yes	characteristic
30	C₈	C₃×Q₁₆	1	1	yes	characteristic
31	C₂×C₃	—	2	1	no	—
32	C₂×C₃	#366	1	1	yes	characteristic
33	C₂²	C₃×Q₃₂	1	1	yes	characteristic
34	C₄	C₃×#107	1	1	yes	characteristic
35	C₄	C₃×D₁₆	1	1	yes	characteristic
36	C₃	#1425	1	1	yes	characteristic, direct product factor, Sylow
37	C₂	—	2	1	no	—
38	C₂	C₃×#366	1	1	yes	characteristic

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

N	H ≅ G/N	type
3. #1425	C₃	direct (N × H)
36. C₃	#1425	direct (N × H)

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