Subgroups — (C₂²⋊C₂₇)⋊C₄ #88392

Order 432.

45 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂²⋊C₂₇	C₂	1	1	yes	maximal, characteristic
2	#3676	—	3	1	no	maximal
3	C₂²⋊C₂₇	C₄	1	1	yes	characteristic, complemented
4	Dic₂₇	—	4	1	no	maximal
5	C₂³×C₉	D₃	1	1	yes	characteristic
6	C₂×Dic₉	—	3	1	no	—
7	C₂×Dic₉	—	3	1	no	—
8	C₂×C₂₇	—	4	1	no	—
9	#217	—	9	1	no	—
10	C₂²×C₉	—	3	1	no	—
11	C₂²×C₉	—	3	1	no	—
12	C₂²×C₉	Dic₃	1	1	yes	characteristic
13	Dic₉	—	6	1	no	—
14	Dic₉	—	6	1	no	—
15	C₂₇	—	4	1	no	Sylow
16	C₂³×C₃	D₉	1	1	yes	characteristic
17	C₂×Dic₃	—	9	1	no	—
18	C₂×Dic₃	—	9	1	no	—
19	C₂×C₉	—	3	1	no	—
20	C₂×C₉	—	3	1	no	—
21	C₂×C₉	S₄	1	1	yes	characteristic
22	C₂²⋊C₄	—	27	1	no	Sylow
23	C₂²×C₃	—	3	1	no	—
24	C₂²×C₃	—	3	1	no	—
25	C₂²×C₃	Dic₉	1	1	yes	characteristic
26	Dic₃	—	18	1	no	—
27	Dic₃	—	18	1	no	—
28	C₉	SL(2,ℤ/4)	1	1	yes	characteristic
29	C₂³	D₂₇	1	1	yes	characteristic
30	C₂×C₄	—	27	1	no	—
31	C₂×C₄	—	27	1	no	—
32	C₂×C₃	—	3	1	no	—
33	C₂×C₃	—	3	1	no	—
34	C₂×C₃	(C₂²⋊C₉)⋊C₂	1	1	yes	characteristic
35	C₂²	—	3	1	no	—
36	C₂²	—	3	1	no	—
37	C₂²	Dic₂₇	1	1	yes	characteristic, complemented
38	C₄	—	54	1	no	—
39	C₄	—	54	1	no	—
40	C₃	(C₂²⋊C₉)⋊C₄	1	1	yes	characteristic
41	C₂	—	3	1	no	—
42	C₂	—	3	1	no	—
43	C₂	(C₂²⋊C₂₇)⋊C₂	1	1	yes	characteristic

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

N	H ≅ G/N	type
3. C₂²⋊C₂₇	C₄	semidirect
37. C₂²	Dic₂₇	semidirect

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