Subgroups — C₂³×C₃⋊Dic₃ #64368

Order 288.

708 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃²	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃⋊Dic₃	C₂	1	14	yes	maximal, direct product factor
3	C₂³×Dic₃	—	3	4	no	maximal
4	C₂³×C₃²	C₄	1	8	yes	complemented
5	C₂³×C₃²	C₂²	1	7	yes	—
6	C₂×C₃⋊Dic₃	C₂²	1	28	yes	direct product factor
7	C₂⁴×C₃	D₃	1	4	yes	—
8	C₂²×Dic₃	—	3	56	no	—
9	C₂²×C₃²	C₂×C₄	1	28	yes	complemented
10	C₂²×C₃²	C₂³	1	7	yes	—
11	C₃⋊Dic₃	C₂³	1	8	yes	direct product factor
12	C₂³×C₄	—	9	1	no	Sylow
13	C₂³×C₃	Dic₃	1	32	yes	complemented
14	C₂³×C₃	C₂×D₃	1	28	yes	—
15	C₂×Dic₃	—	3	112	no	—
16	C₂×C₃²	C₂²×C₄	1	14	yes	complemented
17	C₂×C₃²	C₂⁴	1	1	yes	characteristic
18	C₂⁴	C₃⋊D₃	1	1	yes	characteristic
19	C₂²×C₄	—	9	14	no	—
20	C₂²×C₃	C₂×Dic₃	1	112	yes	complemented
21	C₂²×C₃	C₂²×D₃	1	28	yes	—
22	Dic₃	—	3	32	no	—
23	C₃²	C₂³×C₄	1	1	yes	characteristic, complemented, Sylow
24	C₂³	C₃⋊Dic₃	1	8	yes	direct product factor
25	C₂³	C₂×C₃⋊D₃	1	7	yes	—
26	C₂×C₄	—	9	28	no	—
27	C₂×C₃	C₂²×Dic₃	1	56	yes	complemented
28	C₂×C₃	C₂³×D₃	1	4	yes	—
29	C₂²	C₂×C₃⋊Dic₃	1	28	yes	direct product factor
30	C₂²	C₂²×C₃⋊D₃	1	7	yes	—
31	C₄	—	9	8	no	—
32	C₃	C₂³×Dic₃	1	4	yes	complemented
33	C₂	C₂²×C₃⋊Dic₃	1	14	yes	direct product factor
34	C₂	C₂³×C₃⋊D₃	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.