Subgroups — #63545

Order 288.

61 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₂₄	C₂	1	2	yes	maximal, complemented
2	C₃⋊(C₃⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
3	#826	—	3	2	no	maximal
4	C₃×D₁₂	—	2	2	no	—
5	C₃²×C₈	C₂²	1	1	yes	characteristic
6	C₃×D₈	—	3	2	no	—
7	D₂₄	D₃	1	2	yes	complemented
8	C₃⋊C₁₆	—	3	2	no	—
9	C₃⋊C₁₆	—	6	1	no	—
10	C₂×C₃×D₃	—	4	2	no	—
11	C₃²×C₄	D₄	1	1	yes	characteristic
12	D₁₆	—	9	1	no	Sylow
13	C₃×D₄	—	6	2	no	—
14	D₁₂	—	2	2	no	—
15	C₃×C₈	—	2	1	no	—
16	C₃×C₈	C₂×D₃	1	2	yes	—
17	C₂×C₃²	D₈	1	1	yes	characteristic
18	C₃×D₃	—	8	2	no	—
19	D₈	—	3	2	no	—
20	C₁₆	—	9	1	no	—
21	C₂²×C₃	—	12	2	no	—
22	C₂×D₃	—	4	2	no	—
23	C₃×C₄	—	2	1	no	—
24	C₃×C₄	#67	1	2	yes	—
25	C₃²	D₁₆	1	1	yes	characteristic, complemented, Sylow
26	D₄	—	6	2	no	—
27	C₈	D₃²	1	1	yes	characteristic
28	C₂×C₃	—	2	1	no	—
29	C₂×C₃	—	24	2	no	—
30	C₂×C₃	#213	1	2	yes	—
31	D₃	—	8	2	no	—
32	C₂²	—	12	2	no	—
33	C₄	#625	1	1	yes	characteristic
34	C₃	—	2	1	no	—
35	C₃	#826	1	2	yes	complemented
36	C₂	—	24	2	no	—
37	C₂	#3713	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.