Subgroups — #71960

Order 384.

182 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#564	C₂	1	1	yes	maximal, characteristic, complemented
2	#5067	C₂	1	3	yes	maximal
3	#4543	C₂	1	3	yes	maximal, complemented
4	#1658	—	3	1	no	maximal, Sylow
5	C₃×#125	—	2	6	no	—
6	C₃×#125	C₂²	1	3	yes	—
7	#874	C₂²	1	1	yes	characteristic
8	#809	—	2	6	no	—
9	#803	C₂²	1	3	yes	—
10	#564	D₃	1	1	yes	characteristic, complemented
11	#490	—	3	3	no	—
12	#330	—	3	3	no	—
13	C₂×D₁₂	—	2	3	no	—
14	C₃×C₄⋊C₄	—	2	6	no	—
15	C₃×C₄⋊C₄	—	2	6	no	—
16	C₃×C₄⋊C₄	D₄	1	6	yes	—
17	C₃×C₄²	—	2	2	no	—
18	C₃×C₄²	C₂³	1	1	yes	characteristic
19	C₂×C₃⋊C₈	—	2	3	no	—
20	#127	—	3	1	no	—
21	#125	—	2	6	no	—
22	#125	C₂×D₃	1	3	yes	—
23	#102	—	6	6	no	—
24	#97	—	3	3	no	—
25	C₂²×D₃	—	4	1	no	—
26	C₂×C₃×C₄	—	2	6	no	—
27	C₂×C₃×C₄	C₂×D₄	1	3	yes	—
28	D₁₂	—	4	6	no	—
29	C₃⋊C₈	—	4	3	no	—
30	C₂×D₄	—	6	3	no	—
31	C₂×C₈	—	6	3	no	—
32	C₄⋊C₄	—	2	6	no	—
33	C₄⋊C₄	—	2	6	no	—
34	C₄⋊C₄	#67	1	6	yes	—
35	C₄²	—	2	2	no	—
36	C₄²	C₂²×D₃	1	1	yes	characteristic
37	C₂²×C₃	#120	1	1	yes	characteristic
38	C₂×D₃	—	8	3	no	—
39	C₃×C₄	—	2	3	no	—
40	C₃×C₄	—	4	6	no	—
41	C₂³	—	12	1	no	—
42	D₄	—	12	6	no	—
43	C₂×C₄	—	2	6	no	—
44	C₂×C₄	C₂×#67	1	3	yes	—
45	C₈	—	12	3	no	—
46	C₂×C₃	#454	1	3	yes	—
47	D₃	—	16	1	no	—
48	C₂²	—	24	3	no	—
49	C₂²	#953	1	1	yes	characteristic
50	C₄	—	2	3	no	—
51	C₄	—	4	6	no	—
52	C₃	#1658	1	1	yes	characteristic, complemented, Sylow
53	C₂	—	48	1	no	—
54	C₂	#5245	1	3	yes	—

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.