Subgroups — (C₂²⋊C₉)⋊C₄ #3690

Order 144.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂²⋊C₉	C₂	1	1	yes	maximal, characteristic
2	#217	—	3	1	no	maximal
3	C₂²⋊C₉	C₄	1	1	yes	characteristic, complemented
4	Dic₉	—	4	1	no	maximal
5	C₂³×C₃	D₃	1	1	yes	characteristic
6	C₂×Dic₃	—	3	1	no	—
7	C₂×Dic₃	—	3	1	no	—
8	C₂×C₉	—	4	1	no	—
9	C₂²⋊C₄	—	9	1	no	Sylow
10	C₂²×C₃	—	3	1	no	—
11	C₂²×C₃	—	3	1	no	—
12	C₂²×C₃	Dic₃	1	1	yes	characteristic
13	Dic₃	—	6	1	no	—
14	Dic₃	—	6	1	no	—
15	C₉	—	4	1	no	Sylow
16	C₂³	D₉	1	1	yes	characteristic
17	C₂×C₄	—	9	1	no	—
18	C₂×C₄	—	9	1	no	—
19	C₂×C₃	—	3	1	no	—
20	C₂×C₃	—	3	1	no	—
21	C₂×C₃	S₄	1	1	yes	characteristic
22	C₂²	—	3	1	no	—
23	C₂²	—	3	1	no	—
24	C₂²	Dic₉	1	1	yes	characteristic, complemented
25	C₄	—	18	1	no	—
26	C₄	—	18	1	no	—
27	C₃	SL(2,ℤ/4)	1	1	yes	characteristic
28	C₂	—	3	1	no	—
29	C₂	—	3	1	no	—
30	C₂	(C₂²⋊C₉)⋊C₂	1	1	yes	characteristic

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

N	H ≅ G/N	type
3. C₂²⋊C₉	C₄	semidirect
24. C₂²	Dic₉	semidirect

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