Subgroups — C₃×#333 #4580

Order 192.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄⋊C₈	C₂	1	2	yes	maximal
3	#333	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂×C₃×Q₈	C₄	1	2	yes	—
5	C₂×C₃×C₈	—	2	2	no	—
6	C₃×C₄⋊C₄	—	2	2	no	—
7	C₃×C₄²	C₂²	1	1	yes	characteristic
8	C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
9	C₄⋊C₈	C₂×C₃	1	2	yes	—
10	C₃×Q₈	—	4	2	no	—
11	C₂×C₃×C₄	—	2	2	no	—
12	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
13	C₂×C₃×C₄	D₄	1	2	yes	—
14	C₃×C₈	—	4	2	no	—
15	C₂×Q₈	C₃×C₄	1	2	yes	—
16	C₂×C₈	—	2	2	no	—
17	C₄⋊C₄	—	2	2	no	—
18	C₄²	C₂²×C₃	1	1	yes	characteristic
19	C₂²×C₃	C₂²⋊C₄	1	1	yes	characteristic
20	C₃×C₄	—	2	1	no	—
21	C₃×C₄	—	4	2	no	—
22	C₃×C₄	SD₁₆	1	2	yes	—
23	C₃×C₄	Q₁₆	1	2	yes	—
24	Q₈	—	4	2	no	—
25	C₂×C₄	—	2	2	no	—
26	C₂×C₄	C₂×C₃×C₄	1	1	yes	characteristic
27	C₂×C₄	C₃×D₄	1	2	yes	—
28	C₈	—	4	2	no	—
29	C₂×C₃	#100	1	1	yes	characteristic
30	C₂×C₃	#103	1	2	yes	—
31	C₂²	C₃×C₂²⋊C₄	1	1	yes	characteristic
32	C₄	—	2	1	no	—
33	C₄	—	4	2	no	—
34	C₄	C₃×SD₁₆	1	2	yes	—
35	C₄	C₃×Q₁₆	1	2	yes	—
36	C₃	#333	1	1	yes	characteristic, direct product factor, Sylow
37	C₂	C₃×#100	1	1	yes	characteristic
38	C₂	C₃×#103	1	2	yes	—

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

N	H ≅ G/N	type
3. #333	C₃	direct (N × H)
36. C₃	#333	direct (N × H)

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