Subgroups — #3753

Order 144.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
4	#213	—	3	4	no	maximal
5	C₂²×C₃²	—	2	1	no	—
6	C₂×C₃⋊D₃	—	2	1	no	—
7	C₃²×C₄	C₂²	1	1	yes	characteristic
8	C₃×D₄	D₃	1	4	yes	complemented
9	D₁₂	—	3	4	no	—
10	C₃⋊C₈	—	3	4	no	—
11	C₂×C₃²	—	4	1	no	—
12	C₂×C₃²	D₄	1	1	yes	characteristic
13	C₃⋊D₃	—	4	1	no	—
14	D₈	—	9	1	no	Sylow
15	C₂²×C₃	—	2	4	no	—
16	C₂×D₃	—	6	4	no	—
17	C₃×C₄	C₂×D₃	1	4	yes	—
18	C₃²	D₈	1	1	yes	characteristic, complemented, Sylow
19	D₄	—	9	1	no	—
20	D₄	C₃⋊D₃	1	1	yes	characteristic, complemented
21	C₈	—	9	1	no	—
22	C₂×C₃	—	4	4	no	—
23	C₂×C₃	#67	1	4	yes	—
24	D₃	—	12	4	no	—
25	C₂²	—	2	1	no	—
26	C₂²	—	18	1	no	—
27	C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
28	C₃	#213	1	4	yes	complemented
29	C₂	—	4	1	no	—
30	C₂	—	36	1	no	—
31	C₂	#638	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.