Subgroups — C₃×#104 #847

Order 96.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#41	C₂	1	1	yes	maximal, characteristic
2	C₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄²	C₂	1	1	yes	maximal, characteristic, complemented
4	#104	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₃×Q₈	C₄	1	1	yes	characteristic, complemented
6	C₃×D₄	—	2	1	no	—
7	C₃×D₄	C₄	1	1	yes	characteristic, complemented
8	C₂×C₃×C₄	—	2	1	no	—
9	C₂×C₃×C₄	—	2	1	no	—
10	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
11	C₃×C₈	—	2	1	no	—
12	#41	C₂×C₃	1	1	yes	characteristic
13	M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
14	C₄²	C₂×C₃	1	1	yes	characteristic, complemented
15	C₂²×C₃	—	2	1	no	—
16	C₂²×C₃	D₄	1	1	yes	characteristic
17	C₃×C₄	—	2	2	no	—
18	C₃×C₄	—	2	1	no	—
19	C₃×C₄	C₂×C₄	1	1	yes	characteristic
20	C₃×C₄	D₄	1	1	yes	characteristic
21	Q₈	C₃×C₄	1	1	yes	characteristic, complemented
22	D₄	—	2	1	no	—
23	D₄	C₃×C₄	1	1	yes	characteristic, complemented
24	C₂×C₄	—	2	1	no	—
25	C₂×C₄	—	2	1	no	—
26	C₂×C₄	C₂²×C₃	1	1	yes	characteristic
27	C₈	—	2	1	no	—
28	C₂×C₃	—	2	1	no	—
29	C₂×C₃	—	4	1	no	—
30	C₂×C₃	C₂²⋊C₄	1	1	yes	characteristic
31	C₂²	—	2	1	no	—
32	C₂²	C₃×D₄	1	1	yes	characteristic
33	C₄	—	2	2	no	—
34	C₄	—	2	1	no	—
35	C₄	C₂×C₃×C₄	1	1	yes	characteristic
36	C₄	C₃×D₄	1	1	yes	characteristic
37	C₃	#104	1	1	yes	characteristic, direct product factor, Sylow
38	C₂	—	2	1	no	—
39	C₂	—	4	1	no	—
40	C₂	C₃×C₂²⋊C₄	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.