Subgroups — C₃×Dic₂₄ #63587

Order 288.

53 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Dic₁₂	C₂	1	2	yes	maximal
2	C₃²×C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₃×Q₃₂	—	3	1	no	maximal
4	Dic₂₄	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₃×Dic₆	—	2	2	no	—
6	C₃²×C₈	C₂²	1	1	yes	characteristic
7	C₃×Q₁₆	—	3	2	no	—
8	Dic₁₂	C₂×C₃	1	2	yes	—
9	C₃×C₁₆	—	2	1	no	—
10	C₃×C₁₆	D₃	1	1	yes	characteristic
11	C₃×C₁₆	C₂×C₃	1	1	yes	characteristic
12	C₃²×C₄	D₄	1	1	yes	characteristic
13	C₃×Dic₃	—	4	2	no	—
14	Q₃₂	—	3	1	no	Sylow
15	C₃×Q₈	—	6	2	no	—
16	Dic₆	—	2	2	no	—
17	C₃×C₈	—	2	1	no	—
18	C₃×C₈	C₂×D₃	1	1	yes	characteristic
19	C₃×C₈	C₂²×C₃	1	1	yes	characteristic
20	C₂×C₃²	D₈	1	1	yes	characteristic
21	Q₁₆	—	3	2	no	—
22	C₁₆	C₃×D₃	1	1	yes	characteristic
23	C₃×C₄	—	2	1	no	—
24	C₃×C₄	—	12	2	no	—
25	C₃×C₄	D₁₂	1	1	yes	characteristic
26	C₃×C₄	C₃×D₄	1	1	yes	characteristic
27	Dic₃	—	4	2	no	—
28	C₃²	Q₃₂	1	1	yes	characteristic, complemented, Sylow
29	Q₈	—	6	2	no	—
30	C₈	C₂×C₃×D₃	1	1	yes	characteristic
31	C₂×C₃	—	2	1	no	—
32	C₂×C₃	D₂₄	1	1	yes	characteristic
33	C₂×C₃	C₃×D₈	1	1	yes	characteristic
34	C₄	—	12	2	no	—
35	C₄	C₃×D₁₂	1	1	yes	characteristic
36	C₃	—	2	1	no	—
37	C₃	Dic₂₄	1	1	yes	characteristic, direct product factor
38	C₃	C₃×Q₃₂	1	1	yes	characteristic, complemented
39	C₂	C₃×D₂₄	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.