Subgroups — #64085

Order 288.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₄²	C₂	1	1	yes	maximal, characteristic, complemented
2	#3752	C₂	1	3	yes	maximal
3	#3750	C₂	1	3	yes	maximal, complemented
4	#876	—	3	4	no	maximal
5	C₂²×C₃⋊D₃	C₂²	1	1	yes	characteristic
6	C₂×C₃²×C₄	C₂²	1	3	yes	—
7	C₂×C₃⋊Dic₃	C₂²	1	3	yes	—
8	C₃×C₄²	D₃	1	4	yes	complemented
9	(C₂×D₃)⋊C₄	—	3	12	no	—
10	Dic₃⋊C₄	—	3	12	no	—
11	C₂²×C₃²	C₂³	1	1	yes	characteristic
12	C₂×C₃⋊D₃	—	2	3	no	—
13	C₃²×C₄	—	2	3	no	—
14	C₃⋊Dic₃	—	2	3	no	—
15	#126	—	9	1	no	Sylow
16	C₂²×D₃	—	3	4	no	—
17	C₂×C₃×C₄	C₂×D₃	1	12	yes	—
18	C₂×Dic₃	—	3	12	no	—
19	C₂×C₃²	#41	1	3	yes	—
20	C₃⋊D₃	—	4	1	no	—
21	C₄⋊C₄	—	9	3	no	—
22	C₂²⋊C₄	—	9	3	no	—
23	C₄²	C₃⋊D₃	1	1	yes	characteristic, complemented
24	C₂²×C₃	C₂²×D₃	1	4	yes	—
25	C₂×D₃	—	6	12	no	—
26	C₃×C₄	—	2	12	no	—
27	Dic₃	—	6	12	no	—
28	C₃²	#126	1	1	yes	characteristic, complemented, Sylow
29	C₂³	—	9	1	no	—
30	C₂×C₄	—	9	3	no	—
31	C₂×C₄	C₂×C₃⋊D₃	1	3	yes	—
32	C₂×C₃	#235	1	12	yes	—
33	D₃	—	12	4	no	—
34	C₂²	—	18	3	no	—
35	C₂²	C₂²×C₃⋊D₃	1	1	yes	characteristic
36	C₄	—	2	3	no	—
37	C₄	—	18	3	no	—
38	C₃	#876	1	4	yes	complemented
39	C₂	—	36	1	no	—
40	C₂	#3828	1	3	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.