Subgroups — C₃×C₂²⋊(C₂²⋊C₉) #88906

Order 432.

190 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃²	C₃	1	1	yes	maximal, characteristic
2	C₂²⋊(C₂²⋊C₉)	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₂²⋊C₉	—	4	5	no	maximal
4	C₂³×C₃²	—	3	5	no	—
5	C₂⁴×C₃	C₉	1	3	yes	complemented
6	C₂⁴×C₃	C₃²	1	1	yes	characteristic
7	C₂²×C₃²	—	3	10	no	—
8	C₂²×C₃²	A₄	1	5	yes	—
9	C₂²⋊C₉	—	4	15	no	—
10	C₃×C₉	—	16	1	no	Sylow
11	C₂³×C₃	—	3	15	no	—
12	C₂³×C₃	—	3	5	no	—
13	C₂×C₃²	—	3	5	no	—
14	C₂⁴	C₃×C₉	1	1	yes	characteristic, complemented, Sylow
15	C₂²×C₃	—	3	10	no	—
16	C₂²×C₃	—	3	30	no	—
17	C₂²×C₃	C₂²⋊C₉	1	15	yes	complemented
18	C₂²×C₃	C₃×A₄	1	5	yes	—
19	C₃²	C₂²⋊A₄	1	1	yes	characteristic
20	C₉	—	16	3	no	—
21	C₂³	—	3	5	no	—
22	C₂×C₃	—	3	5	no	—
23	C₂×C₃	—	3	15	no	—
24	C₂²	—	3	10	no	—
25	C₂²	C₃×C₂²⋊C₉	1	5	yes	complemented
26	C₃	C₂²⋊(C₂²⋊C₉)	1	3	yes	direct product factor
27	C₃	C₃×C₂²⋊A₄	1	1	yes	characteristic
28	C₂	—	3	5	no	—

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.