Subgroups — #384⋊C₃ #4634

Order 192.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²⋊C₃	C₂	1	1	yes	maximal, characteristic
2	#384	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
3	C₄×A₄	—	4	1	no	maximal
4	C₄²⋊C₃	C₄	1	1	yes	characteristic, complemented
5	C₂×C₄⋊C₄	—	3	1	no	—
6	C₂×C₄⋊C₄	—	3	1	no	—
7	C₂×C₄²	C₂×C₃	1	1	yes	characteristic
8	C₂×A₄	—	4	1	no	—
9	C₂²×C₄	—	3	1	no	—
10	C₂²×C₄	—	3	1	no	—
11	C₂²×C₄	A₄	1	1	yes	characteristic
12	C₄⋊C₄	—	6	2	no	—
13	C₄⋊C₄	—	6	2	no	—
14	C₄²	—	3	1	no	—
15	C₄²	C₃×C₄	1	1	yes	characteristic, complemented
16	A₄	—	4	1	no	—
17	C₃×C₄	—	16	1	no	—
18	C₂³	C₂×A₄	1	1	yes	characteristic
19	C₂×C₄	—	3	2	no	—
20	C₂×C₄	—	3	2	no	—
21	C₂×C₄	—	3	1	no	—
22	C₂×C₄	—	3	1	no	—
23	C₂×C₄	—	6	1	no	—
24	C₂×C₄	—	6	1	no	—
25	C₂×C₄	—	6	2	no	—
26	C₂×C₃	—	16	1	no	—
27	C₂²	—	3	1	no	—
28	C₂²	—	3	1	no	—
29	C₂²	C₄×A₄	1	1	yes	characteristic
30	C₄	—	3	2	no	—
31	C₄	—	3	2	no	—
32	C₄	—	4	1	no	—
33	C₄	—	12	1	no	—
34	C₃	—	16	1	no	Sylow
35	C₂	—	3	1	no	—
36	C₂	—	3	1	no	—
37	C₂	#127⋊C₃	1	1	yes	characteristic

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.