Subgroups — C₃×#1840 #72555

Order 384.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#376	C₂	1	1	yes	maximal, characteristic
2	C₃×#336	C₂	1	6	yes	maximal
3	#1840	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂²×C₃×C₈	C₂²	1	4	yes	—
5	C₂×C₃×C₄²	C₂²	1	3	yes	—
6	C₃×#95	C₄	1	4	yes	—
7	#376	C₂×C₃	1	1	yes	characteristic
8	#336	C₂×C₃	1	6	yes	—
9	C₂²×C₃×C₄	C₂×C₄	1	6	yes	—
10	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
11	C₂×C₃×C₈	—	2	12	no	—
12	C₃×C₄²	—	2	6	no	—
13	C₂²×C₈	C₂²×C₃	1	4	yes	—
14	C₂×C₄²	C₂²×C₃	1	3	yes	—
15	#95	C₃×C₄	1	4	yes	—
16	C₂³×C₃	C₂²×C₄	1	1	yes	characteristic
17	C₂×C₃×C₄	—	2	6	no	—
18	C₂×C₃×C₄	—	2	12	no	—
19	C₂×C₃×C₄	#41	1	6	yes	—
20	C₃×C₈	—	4	4	no	—
21	C₂²×C₄	C₂×C₃×C₄	1	6	yes	—
22	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
23	C₂×C₈	—	2	12	no	—
24	C₄²	—	2	6	no	—
25	C₂²×C₃	#117	1	3	yes	—
26	C₂²×C₃	#131	1	4	yes	—
27	C₃×C₄	—	4	6	no	—
28	C₃×C₄	#126	1	4	yes	—
29	C₂³	C₂²×C₃×C₄	1	1	yes	characteristic
30	C₂×C₄	—	2	6	no	—
31	C₂×C₄	—	2	12	no	—
32	C₂×C₄	C₃×#41	1	6	yes	—
33	C₈	—	4	4	no	—
34	C₂×C₃	#383	1	1	yes	characteristic
35	C₂×C₃	#433	1	6	yes	—
36	C₂²	C₃×#117	1	3	yes	—
37	C₂²	C₃×#131	1	4	yes	—
38	C₄	—	4	6	no	—
39	C₄	C₃×#126	1	4	yes	—
40	C₃	#1840	1	1	yes	characteristic, direct product factor, Sylow
41	C₂	C₃×#383	1	1	yes	characteristic
42	C₂	C₃×#433	1	6	yes	—

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

N	H ≅ G/N	type
3. #1840	C₃	direct (N × H)
40. C₃	#1840	direct (N × H)

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