Subgroups — #3743

Order 144.

60 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	C₃²×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
4	ΓL(1,𝔽₂₅)	—	3	4	no	maximal
5	C₂×C₃⋊D₃	C₄	1	1	yes	characteristic
6	C₃²×C₄	C₂²	1	1	yes	characteristic
7	C₃⋊Dic₃	C₄	1	1	yes	characteristic
8	C₄×D₃	—	3	4	no	—
9	C₃×C₈	D₃	1	4	yes	complemented
10	C₃⋊C₈	—	3	4	no	—
11	C₂×C₃²	C₂×C₄	1	1	yes	characteristic
12	C₃⋊D₃	—	2	1	no	—
13	M₁₆	—	9	1	no	Sylow
14	C₂×D₃	—	3	4	no	—
15	C₃×C₄	C₂×D₃	1	4	yes	—
16	Dic₃	—	3	4	no	—
17	C₃²	M₁₆	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₄	—	9	1	no	—
19	C₈	—	9	1	no	—
20	C₈	C₃⋊D₃	1	1	yes	characteristic, complemented
21	C₂×C₃	C₄×D₃	1	4	yes	—
22	D₃	—	6	4	no	—
23	C₂²	—	9	1	no	—
24	C₄	—	9	1	no	—
25	C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
26	C₃	ΓL(1,𝔽₂₅)	1	4	yes	complemented
27	C₂	—	18	1	no	—
28	C₂	C₄×C₃⋊D₃	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.