Subgroups — C₃×#364 #4611

Order 192.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×M₃₂	C₂	1	2	yes	maximal
2	C₃×C₄×C₈	C₂	1	1	yes	maximal, characteristic
3	#364	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂×C₃×C₈	C₄	1	1	yes	characteristic
5	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
6	C₃×C₄²	C₄	1	1	yes	characteristic
7	C₃×C₁₆	—	2	2	no	—
8	M₃₂	C₂×C₃	1	2	yes	—
9	C₄×C₈	C₂×C₃	1	1	yes	characteristic
10	C₂×C₃×C₄	—	2	1	no	—
11	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
12	C₃×C₈	C₈	1	2	yes	—
13	C₃×C₈	D₄	1	1	yes	characteristic
14	C₃×C₈	Q₈	1	1	yes	characteristic
15	C₂×C₈	C₃×C₄	1	1	yes	characteristic
16	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
17	C₄²	C₃×C₄	1	1	yes	characteristic
18	C₁₆	—	2	2	no	—
19	C₂²×C₃	M₁₆	1	1	yes	characteristic
20	C₃×C₄	—	2	2	no	—
21	C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
22	C₃×C₄	C₂×C₈	1	1	yes	characteristic
23	C₂×C₄	—	2	1	no	—
24	C₂×C₄	C₂×C₃×C₄	1	1	yes	characteristic
25	C₈	C₃×C₈	1	2	yes	—
26	C₈	C₃×D₄	1	1	yes	characteristic
27	C₈	C₃×Q₈	1	1	yes	characteristic
28	C₂×C₃	—	2	1	no	—
29	C₂×C₃	C₄⋊C₈	1	1	yes	characteristic
30	C₂²	C₃×M₁₆	1	1	yes	characteristic
31	C₄	—	2	2	no	—
32	C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
33	C₄	C₂×C₃×C₈	1	1	yes	characteristic
34	C₃	#364	1	1	yes	characteristic, direct product factor, Sylow
35	C₂	—	2	1	no	—
36	C₂	C₃×C₄⋊C₈	1	1	yes	characteristic

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

N	H ≅ G/N	type
3. #364	C₃	direct (N × H)
34. C₃	#364	direct (N × H)

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