Subgroups — #3713

Order 144.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₂	C₂	1	2	yes	maximal, complemented
2	C₃⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
3	#213	—	3	2	no	maximal
4	C₂×C₃×D₃	—	2	2	no	—
5	C₃²×C₄	C₂²	1	1	yes	characteristic
6	C₃×D₄	—	3	2	no	—
7	D₁₂	D₃	1	2	yes	complemented
8	C₃⋊C₈	—	3	2	no	—
9	C₃⋊C₈	—	6	1	no	—
10	C₂×C₃²	D₄	1	1	yes	characteristic
11	C₃×D₃	—	4	2	no	—
12	D₈	—	9	1	no	Sylow
13	C₂²×C₃	—	6	2	no	—
14	C₂×D₃	—	2	2	no	—
15	C₃×C₄	—	2	1	no	—
16	C₃×C₄	C₂×D₃	1	2	yes	—
17	C₃²	D₈	1	1	yes	characteristic, complemented, Sylow
18	D₄	—	3	2	no	—
19	C₈	—	9	1	no	—
20	C₂×C₃	—	2	1	no	—
21	C₂×C₃	—	12	2	no	—
22	C₂×C₃	#67	1	2	yes	—
23	D₃	—	4	2	no	—
24	C₂²	—	6	2	no	—
25	C₄	D₃²	1	1	yes	characteristic
26	C₃	—	2	1	no	—
27	C₃	#213	1	2	yes	complemented
28	C₂	—	12	2	no	—
29	C₂	#625	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.