Subgroups — #64289

Order 288.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3832	C₂	1	1	yes	maximal, characteristic
2	#3788	C₂	1	3	yes	maximal, complemented
3	#3787	C₂	1	3	yes	maximal, complemented
4	C₃²×Q₈	C₄	1	1	yes	characteristic
5	C₄⋊(C₃⋊D₃)	C₄	1	3	yes	—
6	C₄×C₃⋊D₃	C₂²	1	3	yes	—
7	#622	C₂²	1	1	yes	characteristic
8	#622	C₂²	1	3	yes	—
9	#239	—	6	2	no	—
10	C₂×C₃⋊D₃	C₂×C₄	1	3	yes	—
11	C₃²×C₄	C₂×C₄	1	3	yes	—
12	C₃⋊Dic₃	C₂³	1	1	yes	characteristic
13	#131	—	9	1	no	maximal, Sylow
14	C₃×Q₈	—	2	2	no	—
15	D₁₂	—	6	6	no	—
16	C₄×D₃	—	6	6	no	—
17	C₂×C₃²	C₂²×C₄	1	1	yes	characteristic
18	C₃⋊D₃	—	2	3	no	—
19	#41	—	9	1	no	—
20	M₁₆	—	9	3	no	—
21	C₂×C₈	—	9	3	no	—
22	C₂×D₃	—	6	6	no	—
23	C₃×C₄	—	2	6	no	—
24	Dic₃	—	6	2	no	—
25	C₃²	#131	1	1	yes	characteristic, complemented, Sylow
26	Q₈	#157	1	1	yes	characteristic
27	D₄	—	9	3	no	—
28	C₂×C₄	—	9	3	no	—
29	C₈	—	9	1	no	—
30	C₈	—	9	3	no	—
31	C₂×C₃	—	2	2	no	—
32	D₃	—	12	6	no	—
33	C₂²	—	9	3	no	—
34	C₄	—	9	1	no	—
35	C₄	C₂×#157	1	3	yes	—
36	C₃	—	2	2	no	—
37	C₂	—	18	3	no	—
38	C₂	C₂²×#157	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.