Subgroups — #3750

Order 144.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic
4	Dic₃⋊C₄	—	3	4	no	maximal
5	C₂²×C₃²	C₂²	1	1	yes	characteristic
6	C₃²×C₄	—	2	1	no	—
7	C₃⋊Dic₃	—	2	1	no	—
8	C₃⋊Dic₃	C₄	1	2	yes	complemented
9	C₂×C₃×C₄	D₃	1	4	yes	—
10	C₂×Dic₃	—	3	4	no	—
11	C₂×Dic₃	—	3	4	no	—
12	C₂×C₃²	C₂×C₄	1	1	yes	characteristic
13	C₂×C₃²	D₄	1	1	yes	characteristic
14	C₂×C₃²	Q₈	1	1	yes	characteristic
15	C₄⋊C₄	—	9	1	no	Sylow
16	C₂²×C₃	C₂×D₃	1	4	yes	—
17	C₃×C₄	—	2	4	no	—
18	Dic₃	—	3	8	no	—
19	Dic₃	—	6	4	no	—
20	C₃²	C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₄	—	9	1	no	—
22	C₂×C₄	—	9	1	no	—
23	C₂×C₄	C₃⋊D₃	1	1	yes	characteristic
24	C₂×C₃	Dic₆	1	4	yes	—
25	C₂×C₃	C₄×D₃	1	4	yes	—
26	C₂×C₃	#67	1	4	yes	—
27	C₂²	C₂×C₃⋊D₃	1	1	yes	characteristic
28	C₄	—	2	1	no	—
29	C₄	—	9	2	no	—
30	C₄	—	18	1	no	—
31	C₃	Dic₃⋊C₄	1	4	yes	complemented
32	C₂	#634	1	1	yes	characteristic
33	C₂	C₄×C₃⋊D₃	1	1	yes	characteristic
34	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.