Subgroups — #3718

Order 144.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Dic₆	C₂	1	2	yes	maximal
2	C₃⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	#216	—	3	2	no	maximal
4	C₃²×C₄	C₂²	1	1	yes	characteristic
5	C₃×Dic₃	—	2	2	no	—
6	C₃×Q₈	—	3	2	no	—
7	Dic₆	D₃	1	2	yes	—
8	C₃⋊C₈	—	3	2	no	—
9	C₃⋊C₈	—	6	1	no	—
10	C₂×C₃²	D₄	1	1	yes	characteristic
11	Q₁₆	—	9	1	no	Sylow
12	C₃×C₄	—	2	1	no	—
13	C₃×C₄	—	6	2	no	—
14	C₃×C₄	C₂×D₃	1	2	yes	—
15	Dic₃	—	2	2	no	—
16	C₃²	Q₁₆	1	1	yes	characteristic, complemented, Sylow
17	Q₈	—	3	2	no	—
18	C₈	—	9	1	no	—
19	C₂×C₃	—	2	1	no	—
20	C₂×C₃	#67	1	2	yes	—
21	C₄	—	6	2	no	—
22	C₄	D₃²	1	1	yes	characteristic
23	C₃	—	2	1	no	—
24	C₃	#216	1	2	yes	complemented
25	C₂	#625	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
16. C₃²	Q₁₆	semidirect
24. C₃	#216	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.