Subgroups — #88363

Order 432.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₂₇	C₂	1	1	yes	maximal, characteristic
2	C₂₇⋊C₈	C₂	1	2	yes	maximal, complemented
3	#3667	—	3	1	no	maximal
4	C₂²×C₂₇	C₄	1	1	yes	characteristic
5	C₄×C₂₇	C₄	1	1	yes	characteristic
6	C₄×C₂₇	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₉	D₃	1	1	yes	characteristic
8	C₉⋊C₈	—	3	2	no	—
9	C₂×C₂₇	—	2	1	no	—
10	C₂×C₂₇	C₂×C₄	1	1	yes	characteristic
11	#208	—	9	1	no	—
12	C₂²×C₉	Dic₃	1	1	yes	characteristic
13	C₄×C₉	Dic₃	1	1	yes	characteristic
14	C₄×C₉	C₂×D₃	1	1	yes	characteristic
15	C₂₇	M₁₆	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₃×C₄	D₉	1	1	yes	characteristic
17	C₃⋊C₈	—	9	2	no	—
18	C₂×C₉	—	2	1	no	—
19	C₂×C₉	C₂×Dic₃	1	1	yes	characteristic
20	M₁₆	—	27	1	no	Sylow
21	C₂²×C₃	Dic₉	1	1	yes	characteristic
22	C₃×C₄	Dic₉	1	1	yes	characteristic
23	C₃×C₄	C₂×D₉	1	1	yes	characteristic
24	C₉	#208	1	1	yes	characteristic
25	C₂×C₄	D₂₇	1	1	yes	characteristic
26	C₈	—	27	2	no	—
27	C₂×C₃	—	2	1	no	—
28	C₂×C₃	C₂×Dic₉	1	1	yes	characteristic
29	C₂²	Dic₂₇	1	1	yes	characteristic
30	C₄	Dic₂₇	1	1	yes	characteristic
31	C₄	C₂×D₂₇	1	1	yes	characteristic
32	C₃	#3667	1	1	yes	characteristic
33	C₂	—	2	1	no	—
34	C₂	C₂×Dic₂₇	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. C₂₇⋊C₈	C₂	semidirect
15. C₂₇	M₁₆	semidirect

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