Subgroups — #3757

Order 144.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃²	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃⋊Dic₃	C₂	1	2	yes	maximal, complemented
3	#217	—	3	4	no	maximal
4	C₂²×C₃²	—	2	2	no	—
5	C₂²×C₃²	C₄	1	2	yes	complemented
6	C₂²×C₃²	C₂²	1	1	yes	characteristic
7	C₃⋊Dic₃	—	2	2	no	—
8	C₂³×C₃	D₃	1	4	yes	—
9	C₂×Dic₃	—	3	8	no	—
10	C₂×C₃²	—	2	2	no	—
11	C₂×C₃²	C₂×C₄	1	1	yes	characteristic
12	C₂×C₃²	D₄	1	2	yes	—
13	C₂²⋊C₄	—	9	1	no	Sylow
14	C₂²×C₃	—	2	8	no	—
15	C₂²×C₃	Dic₃	1	8	yes	complemented
16	C₂²×C₃	C₂×D₃	1	4	yes	—
17	Dic₃	—	6	8	no	—
18	C₃²	C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
19	C₂³	C₃⋊D₃	1	1	yes	characteristic
20	C₂×C₄	—	9	2	no	—
21	C₂×C₃	—	2	8	no	—
22	C₂×C₃	C₂×Dic₃	1	4	yes	—
23	C₂×C₃	#67	1	8	yes	—
24	C₂²	—	2	2	no	—
25	C₂²	C₃⋊Dic₃	1	2	yes	complemented
26	C₂²	C₂×C₃⋊D₃	1	1	yes	characteristic
27	C₄	—	18	2	no	—
28	C₃	#217	1	4	yes	complemented
29	C₂	—	2	2	no	—
30	C₂	C₂×C₃⋊Dic₃	1	1	yes	characteristic
31	C₂	#638	1	2	yes	—

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.