Subgroups — #88368

Order 432.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×C₂₇	C₂	1	1	yes	maximal, characteristic
2	Dic₅₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#3672	—	3	1	no	maximal
5	C₂²×C₂₇	—	2	1	no	—
6	C₄×C₂₇	C₂²	1	1	yes	characteristic
7	Dic₂₇	—	2	1	no	—
8	D₄×C₉	D₃	1	1	yes	characteristic
9	Dic₁₈	—	3	1	no	—
10	C₉⋊C₈	—	3	1	no	—
11	C₂×C₂₇	—	4	1	no	—
12	C₂×C₂₇	D₄	1	1	yes	characteristic
13	#214	—	9	1	no	—
14	C₂²×C₉	—	2	1	no	—
15	C₄×C₉	C₂×D₃	1	1	yes	characteristic
16	Dic₉	—	6	1	no	—
17	C₂₇	SD₁₆	1	1	yes	characteristic, complemented, Sylow
18	C₃×D₄	D₉	1	1	yes	characteristic
19	Dic₆	—	9	1	no	—
20	C₃⋊C₈	—	9	1	no	—
21	C₂×C₉	—	4	1	no	—
22	C₂×C₉	#67	1	1	yes	characteristic
23	SD₁₆	—	27	1	no	Sylow
24	C₂²×C₃	—	2	1	no	—
25	C₃×C₄	C₂×D₉	1	1	yes	characteristic
26	Dic₃	—	18	1	no	—
27	C₉	#214	1	1	yes	characteristic
28	Q₈	—	27	1	no	—
29	D₄	D₂₇	1	1	yes	characteristic
30	C₈	—	27	1	no	—
31	C₂×C₃	—	4	1	no	—
32	C₂×C₃	#611	1	1	yes	characteristic
33	C₂²	—	2	1	no	—
34	C₄	—	54	1	no	—
35	C₄	C₂×D₂₇	1	1	yes	characteristic
36	C₃	#3672	1	1	yes	characteristic
37	C₂	—	4	1	no	—
38	C₂	#6171	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.