Subgroups — C₉×Q₃₂ #63415

Order 288.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×Q₁₆	C₂	1	2	yes	maximal
2	C₉×C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₃×Q₃₂	C₃	1	1	yes	maximal, characteristic
4	Q₈×C₉	—	2	2	no	—
5	C₈×C₉	C₂²	1	1	yes	characteristic
6	C₃×Q₁₆	C₂×C₃	1	2	yes	—
7	C₃×C₁₆	C₂×C₃	1	1	yes	characteristic
8	C₄×C₉	—	4	2	no	—
9	C₄×C₉	D₄	1	1	yes	characteristic
10	Q₃₂	C₉	1	1	yes	characteristic, direct product factor, Sylow
11	C₃×Q₈	—	2	2	no	—
12	C₃×C₈	C₂²×C₃	1	1	yes	characteristic
13	C₂×C₉	D₈	1	1	yes	characteristic
14	Q₁₆	C₂×C₉	1	2	yes	—
15	C₁₆	C₂×C₉	1	1	yes	characteristic
16	C₃×C₄	—	4	2	no	—
17	C₃×C₄	C₃×D₄	1	1	yes	characteristic
18	C₉	Q₃₂	1	1	yes	characteristic, direct product factor, Sylow
19	Q₈	—	2	2	no	—
20	C₈	C₂²×C₉	1	1	yes	characteristic
21	C₂×C₃	C₃×D₈	1	1	yes	characteristic
22	C₄	—	4	2	no	—
23	C₄	D₄×C₉	1	1	yes	characteristic
24	C₃	C₃×Q₃₂	1	1	yes	characteristic
25	C₂	C₉×D₈	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
10. Q₃₂	C₉	direct (N × H)
18. C₉	Q₃₂	direct (N × H)

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.