Subgroups — C₃×#366 #4613

Order 192.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₃×#107	C₂	1	2	yes	maximal
3	#366	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
5	C₃×C₄⋊C₄	—	2	2	no	—
6	C₃×C₁₆	C₄	1	2	yes	complemented
7	C₂×C₁₆	C₂×C₃	1	1	yes	characteristic
8	#107	C₂×C₃	1	2	yes	—
9	C₂×C₃×C₄	—	4	2	no	—
10	C₂×C₃×C₄	D₄	1	1	yes	characteristic
11	C₃×C₈	C₂×C₄	1	1	yes	characteristic
12	C₃×C₈	Q₈	1	1	yes	characteristic
13	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
14	C₄⋊C₄	—	2	2	no	—
15	C₁₆	C₃×C₄	1	2	yes	complemented
16	C₂²×C₃	D₈	1	1	yes	characteristic
17	C₃×C₄	—	8	2	no	—
18	C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
19	C₃×C₄	Q₁₆	1	1	yes	characteristic
20	C₂×C₄	—	4	2	no	—
21	C₂×C₄	C₃×D₄	1	1	yes	characteristic
22	C₈	C₂×C₃×C₄	1	1	yes	characteristic
23	C₈	C₃×Q₈	1	1	yes	characteristic
24	C₂×C₃	#107	1	1	yes	characteristic
25	C₂×C₃	D₁₆	1	1	yes	characteristic
26	C₂×C₃	Q₃₂	1	1	yes	characteristic
27	C₂²	C₃×D₈	1	1	yes	characteristic
28	C₄	—	8	2	no	—
29	C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
30	C₄	C₃×Q₁₆	1	1	yes	characteristic
31	C₃	#366	1	1	yes	characteristic, direct product factor, Sylow
32	C₂	C₃×#107	1	1	yes	characteristic
33	C₂	C₃×D₁₆	1	1	yes	characteristic
34	C₂	C₃×Q₃₂	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.