Subgroups — #3788

Order 144.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	#622	C₂	1	2	yes	maximal, complemented
3	C₂×C₃⋊D₃	C₄	1	1	yes	characteristic
4	C₃²×C₄	C₄	1	1	yes	characteristic
5	C₃⋊Dic₃	C₂²	1	1	yes	characteristic
6	C₄×D₃	—	6	2	no	—
7	C₂×C₃²	C₂×C₄	1	1	yes	characteristic
8	C₃⋊D₃	—	2	1	no	—
9	M₁₆	—	9	1	no	maximal, Sylow
10	C₂×D₃	—	6	2	no	—
11	C₃×C₄	—	2	2	no	—
12	Dic₃	—	6	2	no	—
13	C₃²	M₁₆	1	1	yes	characteristic, complemented, Sylow
14	C₂×C₄	—	9	1	no	—
15	C₈	—	9	2	no	—
16	C₂×C₃	—	2	2	no	—
17	D₃	—	6	4	no	—
18	C₂²	—	9	1	no	—
19	C₄	—	9	1	no	—
20	C₄	#157	1	1	yes	characteristic
21	C₃	—	2	2	no	—
22	C₂	—	18	1	no	—
23	C₂	C₂×#157	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. #622	C₂	semidirect
13. C₃²	M₁₆	semidirect

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