Subgroups — #64228

Order 288.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3797	C₂	1	2	yes	maximal
2	#3787	C₂	1	1	yes	maximal, characteristic
3	#3776	C₂	1	4	yes	maximal, complemented
4	C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
5	C₃×Dic₆	—	2	2	no	—
6	#627	C₂²	1	4	yes	—
7	#624	—	2	2	no	—
8	#622	C₂²	1	2	yes	—
9	D₃×Q₈	—	6	2	no	—
10	C₂×C₃⋊D₃	D₄	1	1	yes	characteristic
11	C₃²×C₄	D₄	1	1	yes	characteristic
12	C₃⋊Dic₃	C₂³	1	1	yes	characteristic
13	C₃×Dic₃	—	2	4	no	—
14	C₂×Q₁₆	—	9	1	no	maximal, Sylow
15	C₃×Q₈	—	6	2	no	—
16	C₄×D₃	—	6	2	no	—
17	C₄×D₃	—	6	4	no	—
18	Dic₆	—	2	2	no	—
19	Dic₆	—	6	4	no	—
20	C₂×C₃²	C₂×D₄	1	1	yes	characteristic
21	C₃⋊D₃	Q₁₆	1	2	yes	complemented
22	C₂×Q₈	—	9	2	no	—
23	Q₁₆	—	9	4	no	—
24	C₂×C₈	—	9	1	no	—
25	C₂×D₃	—	6	2	no	—
26	C₃×C₄	—	2	2	no	—
27	C₃×C₄	—	6	4	no	—
28	Dic₃	—	2	4	no	—
29	Dic₃	—	6	2	no	—
30	C₃²	C₂×Q₁₆	1	1	yes	characteristic, complemented, Sylow
31	Q₈	—	6	2	no	—
32	Q₈	—	9	4	no	—
33	C₂×C₄	—	9	1	no	—
34	C₂×C₄	—	18	2	no	—
35	C₈	—	9	2	no	—
36	C₂×C₃	—	2	2	no	—
37	D₃	—	6	4	no	—
38	C₂²	—	9	1	no	—
39	C₄	—	6	4	no	—
40	C₄	—	9	1	no	—
41	C₄	GO⁺(4,𝔽₂)	1	1	yes	characteristic
42	C₃	—	2	2	no	—
43	C₂	—	9	2	no	—
44	C₂	C₂×GO⁺(4,𝔽₂)	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.