Subgroups — #68049

Order 384.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#4685	C₂	1	3	yes	maximal
2	C₃×C₈²	C₂	1	1	yes	maximal, characteristic, complemented
3	#4454	C₂	1	3	yes	maximal, complemented
4	#1454	—	3	1	no	maximal, Sylow
5	C₄²×D₃	C₂²	1	1	yes	characteristic
6	C₃×C₄×C₈	C₂²	1	3	yes	—
7	(C₂×D₃)⋊C₈	C₄	1	6	yes	—
8	Dic₃⋊C₈	C₄	1	6	yes	—
9	C₄×C₃⋊C₈	C₂²	1	3	yes	—
10	#431	—	3	3	no	—
11	#322	—	3	3	no	—
12	C₈²	D₃	1	1	yes	characteristic, complemented
13	C₂×C₄×D₃	C₂×C₄	1	3	yes	—
14	C₂×C₃×C₈	C₂×C₄	1	6	yes	—
15	C₃×C₄²	C₂³	1	1	yes	characteristic
16	C₄×Dic₃	C₂×C₄	1	3	yes	—
17	C₂×C₃⋊C₈	C₂×C₄	1	6	yes	—
18	C₂×C₄²	—	3	1	no	—
19	C₄⋊C₈	—	3	6	no	—
20	C₂²⋊C₈	—	3	6	no	—
21	C₄×C₈	—	3	3	no	—
22	C₄×C₈	C₂×D₃	1	3	yes	—
23	C₂²×D₃	C₄²	1	1	yes	characteristic
24	C₂×C₃×C₄	C₂²×C₄	1	3	yes	—
25	C₂×Dic₃	C₄²	1	3	yes	—
26	C₄×D₃	—	2	6	no	—
27	C₃×C₈	—	2	6	no	—
28	C₃⋊C₈	—	2	6	no	—
29	C₂²×C₄	—	3	3	no	—
30	C₂×C₈	—	3	6	no	—
31	C₂×C₈	C₄×D₃	1	6	yes	—
32	C₄²	—	3	3	no	—
33	C₄²	C₂²×D₃	1	1	yes	characteristic
34	C₂²×C₃	C₂×C₄²	1	1	yes	characteristic
35	C₂×D₃	—	2	3	no	—
36	C₃×C₄	#131	1	6	yes	—
37	Dic₃	—	2	3	no	—
38	C₂³	—	3	1	no	—
39	C₂×C₄	—	3	3	no	—
40	C₂×C₄	—	6	6	no	—
41	C₂×C₄	C₂×C₄×D₃	1	3	yes	—
42	C₈	—	2	6	no	—
43	C₈	—	6	6	no	—
44	C₂×C₃	#405	1	3	yes	—
45	D₃	—	4	1	no	—
46	C₂²	—	6	3	no	—
47	C₂²	C₄²×D₃	1	1	yes	characteristic
48	C₄	—	6	3	no	—
49	C₄	#901	1	6	yes	—
50	C₃	#1454	1	1	yes	characteristic, complemented, Sylow
51	C₂	—	12	1	no	—
52	C₂	#4689	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.