Subgroups — #63764

Order 288.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	#3708	C₂	1	2	yes	maximal, complemented
3	C₄×C₃⋊D₃	C₄	1	1	yes	characteristic
4	C₃²×C₈	C₄	1	1	yes	characteristic
5	C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
6	D₃×C₈	—	6	2	no	—
7	C₂×C₃⋊D₃	C₈	1	1	yes	characteristic
8	C₃²×C₄	C₂×C₄	1	1	yes	characteristic
9	C₃⋊Dic₃	C₈	1	1	yes	characteristic
10	C₂×C₁₆	—	9	1	no	maximal, Sylow
11	C₄×D₃	—	6	2	no	—
12	C₃×C₈	—	2	2	no	—
13	C₃⋊C₈	—	6	2	no	—
14	C₂×C₃²	C₂×C₈	1	1	yes	characteristic
15	C₃⋊D₃	C₁₆	1	2	yes	complemented
16	C₂×C₈	—	9	1	no	—
17	C₁₆	—	9	2	no	—
18	C₂×D₃	—	6	2	no	—
19	C₃×C₄	—	2	2	no	—
20	Dic₃	—	6	2	no	—
21	C₃²	C₂×C₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₄	—	9	1	no	—
23	C₈	—	9	1	no	—
24	C₈	#157	1	1	yes	characteristic
25	C₂×C₃	—	2	2	no	—
26	D₃	—	6	4	no	—
27	C₂²	—	9	1	no	—
28	C₄	—	9	1	no	—
29	C₄	C₂×#157	1	1	yes	characteristic
30	C₃	—	2	2	no	—
31	C₂	—	9	2	no	—
32	C₂	#3787	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.