Subgroups — C₃×#384 #5258

Order 192.

186 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄⋊C₄	C₂	1	6	yes	maximal
2	C₂×C₃×C₄²	C₂	1	1	yes	maximal, characteristic
3	#384	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂²×C₃×C₄	C₂²	1	4	yes	—
5	C₂²×C₃×C₄	C₂²	1	3	yes	—
6	C₃×C₄⋊C₄	—	2	12	no	—
7	C₃×C₄²	C₄	1	4	yes	complemented
8	C₂×C₄⋊C₄	C₂×C₃	1	6	yes	—
9	C₂×C₄²	C₂×C₃	1	1	yes	characteristic
10	C₂³×C₃	C₂³	1	1	yes	characteristic
11	C₂×C₃×C₄	—	2	12	no	—
12	C₂×C₃×C₄	C₂×C₄	1	6	yes	—
13	C₂×C₃×C₄	D₄	1	6	yes	—
14	C₂×C₃×C₄	Q₈	1	6	yes	—
15	C₂²×C₄	C₂²×C₃	1	4	yes	—
16	C₂²×C₄	C₂²×C₃	1	3	yes	—
17	C₄⋊C₄	—	2	12	no	—
18	C₄²	C₃×C₄	1	4	yes	complemented
19	C₂²×C₃	C₂²×C₄	1	1	yes	characteristic
20	C₂²×C₃	C₂×D₄	1	3	yes	—
21	C₂²×C₃	C₂×Q₈	1	3	yes	—
22	C₃×C₄	—	4	4	no	—
23	C₃×C₄	C₄⋊C₄	1	12	yes	complemented
24	C₂³	C₂³×C₃	1	1	yes	characteristic
25	C₂×C₄	—	2	12	no	—
26	C₂×C₄	C₂×C₃×C₄	1	6	yes	—
27	C₂×C₄	C₃×D₄	1	6	yes	—
28	C₂×C₄	C₃×Q₈	1	6	yes	—
29	C₂×C₃	C₂×C₄⋊C₄	1	3	yes	—
30	C₂×C₃	#127	1	1	yes	characteristic
31	C₂×C₃	C₄⋊Q₈	1	3	yes	—
32	C₂²	C₂²×C₃×C₄	1	1	yes	characteristic
33	C₂²	C₂×C₃×D₄	1	3	yes	—
34	C₂²	C₂×C₃×Q₈	1	3	yes	—
35	C₄	—	4	4	no	—
36	C₄	C₃×C₄⋊C₄	1	12	yes	complemented
37	C₃	#384	1	1	yes	characteristic, direct product factor, Sylow
38	C₂	C₂×C₃×C₄⋊C₄	1	3	yes	—
39	C₂	C₃×#127	1	1	yes	characteristic
40	C₂	C₃×C₄⋊Q₈	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.