Subgroups — C₉×#106 #63408

Order 288.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×C₉	C₂	1	1	yes	maximal, characteristic
2	C₉×C₄⋊C₄	C₂	1	2	yes	maximal
3	C₃×#106	C₃	1	1	yes	maximal, characteristic
4	C₂×C₄×C₉	—	2	2	no	—
5	C₂×C₄×C₉	C₂²	1	1	yes	characteristic
6	C₈×C₉	C₄	1	2	yes	complemented
7	C₂×C₃×C₈	C₂×C₃	1	1	yes	characteristic
8	C₃×C₄⋊C₄	C₂×C₃	1	2	yes	—
9	C₂²×C₉	D₄	1	1	yes	characteristic
10	C₄×C₉	—	4	2	no	—
11	C₄×C₉	C₂×C₄	1	1	yes	characteristic
12	C₄×C₉	Q₈	1	1	yes	characteristic
13	#106	C₉	1	1	yes	characteristic, direct product factor, Sylow
14	C₂×C₃×C₄	—	2	2	no	—
15	C₂×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
16	C₃×C₈	C₃×C₄	1	2	yes	—
17	C₂×C₉	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₉	SD₁₆	1	2	yes	—
19	C₂×C₈	C₂×C₉	1	1	yes	characteristic
20	C₄⋊C₄	C₂×C₉	1	2	yes	—
21	C₂²×C₃	C₃×D₄	1	1	yes	characteristic
22	C₃×C₄	—	4	2	no	—
23	C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
24	C₃×C₄	C₃×Q₈	1	1	yes	characteristic
25	C₉	#106	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×C₄	—	2	2	no	—
27	C₂×C₄	C₂²×C₉	1	1	yes	characteristic
28	C₈	C₄×C₉	1	2	yes	complemented
29	C₂×C₃	C₃×C₄⋊C₄	1	1	yes	characteristic
30	C₂×C₃	C₃×SD₁₆	1	2	yes	—
31	C₂²	D₄×C₉	1	1	yes	characteristic
32	C₄	—	4	2	no	—
33	C₄	C₂×C₄×C₉	1	1	yes	characteristic
34	C₄	Q₈×C₉	1	1	yes	characteristic
35	C₃	C₃×#106	1	1	yes	characteristic
36	C₂	C₉×C₄⋊C₄	1	1	yes	characteristic
37	C₂	C₉×SD₁₆	1	2	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.