Subgroups — C₃²×#3926 #13083900

Order 1440.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₃×#3926	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₅×C₈	C₄	1	1	yes	characteristic
4	C₃²×C₃₂	—	5	1	no	maximal, Hall
5	C₃×C₅×C₁₆	C₂×C₃	1	4	yes	—
6	C₃²×C₄×C₅	C₈	1	1	yes	characteristic
7	#3926	C₃²	1	1	yes	characteristic, direct product factor, Hall
8	C₃²×C₁₆	D₅	1	1	yes	characteristic
9	C₃×C₅×C₈	C₃×C₄	1	4	yes	—
10	C₃×C₃₂	—	5	4	no	—
11	C₂×C₃²×C₅	C₁₆	1	1	yes	characteristic
12	C₅×C₁₆	C₂×C₃²	1	1	yes	characteristic
13	C₃²×C₈	Dic₅	1	1	yes	characteristic
14	C₃×C₄×C₅	C₃×C₈	1	4	yes	—
15	C₃×C₁₆	C₃×D₅	1	4	yes	—
16	C₃²×C₅	C₃₂	1	1	yes	characteristic, complemented, Hall
17	C₅×C₈	C₃²×C₄	1	1	yes	characteristic
18	C₃²×C₄	#168	1	1	yes	characteristic
19	C₃₂	—	5	1	no	Sylow
20	C₂×C₃×C₅	C₃×C₁₆	1	4	yes	—
21	C₃×C₈	C₃×Dic₅	1	4	yes	—
22	C₄×C₅	C₃²×C₈	1	1	yes	characteristic
23	C₂×C₃²	#672	1	1	yes	characteristic
24	C₁₆	C₃²×D₅	1	1	yes	characteristic
25	C₃×C₅	C₃×C₃₂	1	4	yes	complemented
26	C₃×C₄	C₃×#168	1	4	yes	—
27	C₂×C₅	C₃²×C₁₆	1	1	yes	characteristic
28	C₃²	#3926	1	1	yes	characteristic, direct product factor, Sylow
29	C₈	C₃²×Dic₅	1	1	yes	characteristic
30	C₂×C₃	C₃×#672	1	4	yes	—
31	C₅	C₃²×C₃₂	1	1	yes	characteristic, complemented, Sylow
32	C₄	C₃²×#168	1	1	yes	characteristic
33	C₃	C₃×#3926	1	4	yes	direct product factor
34	C₂	C₃²×#672	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.