Subgroups — C₃²×Dic₆ #6298

Order 216.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₄	C₂	1	1	yes	maximal, characteristic
2	C₃²×Dic₃	C₂	1	2	yes	maximal
3	C₃²×Q₈	—	3	1	no	maximal
4	C₃×Dic₆	C₃	1	4	yes	maximal, direct product factor
5	C₂×C₃³	C₂²	1	1	yes	characteristic
6	C₃²×C₄	—	2	4	no	—
7	C₃²×C₄	—	3	2	no	—
8	C₃²×C₄	D₃	1	1	yes	characteristic
9	C₃²×C₄	C₂×C₃	1	4	yes	—
10	C₃×Dic₃	C₂×C₃	1	8	yes	—
11	C₃³	Q₈	1	1	yes	characteristic, complemented, Sylow
12	C₃×Q₈	—	3	4	no	—
13	Dic₆	C₃²	1	1	yes	characteristic, direct product factor
14	C₂×C₃²	—	2	4	no	—
15	C₂×C₃²	C₂×D₃	1	1	yes	characteristic
16	C₂×C₃²	C₂²×C₃	1	4	yes	—
17	C₃×C₄	—	2	4	no	—
18	C₃×C₄	—	3	8	no	—
19	C₃×C₄	C₃×D₃	1	4	yes	—
20	C₃×C₄	C₂×C₃²	1	1	yes	characteristic
21	Dic₃	C₂×C₃²	1	2	yes	—
22	C₃²	—	2	4	no	—
23	C₃²	Dic₆	1	1	yes	characteristic, direct product factor
24	C₃²	C₃×Q₈	1	4	yes	complemented
25	Q₈	—	3	1	no	Sylow
26	C₂×C₃	—	2	4	no	—
27	C₂×C₃	C₂×C₃×D₃	1	4	yes	—
28	C₂×C₃	C₂²×C₃²	1	1	yes	characteristic
29	C₄	—	3	2	no	—
30	C₄	C₃²×D₃	1	1	yes	characteristic
31	C₃	—	2	4	no	—
32	C₃	C₃×Dic₆	1	4	yes	direct product factor
33	C₃	C₃²×Q₈	1	1	yes	characteristic, complemented
34	C₂	C₂×C₃²×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.