Subgroups — C₂×D₃×C₂₇ #66374

Order 324.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₂₇	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₂₇	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₃×C₉	C₃	1	1	yes	maximal, characteristic
4	C₂²×C₂₇	—	3	1	no	maximal
5	C₃×C₂₇	C₂²	1	1	yes	characteristic, complemented, Sylow
6	C₂×C₃×C₉	C₂×C₃	1	1	yes	characteristic
7	D₃×C₉	C₂×C₃	1	2	yes	—
8	C₂×C₂₇	—	2	1	no	—
9	C₂×C₂₇	—	3	2	no	—
10	C₂×C₂₇	D₃	1	1	yes	characteristic, direct product factor
11	C₂×C₃×D₃	C₉	1	1	yes	characteristic
12	C₂²×C₉	—	3	1	no	—
13	C₃×C₉	C₂²×C₃	1	1	yes	characteristic
14	C₂₇	—	2	1	no	—
15	C₂₇	C₂×D₃	1	1	yes	characteristic, direct product factor
16	C₂×C₃²	C₂×C₉	1	1	yes	characteristic
17	C₃×D₃	C₂×C₉	1	2	yes	—
18	C₂×C₉	—	2	1	no	—
19	C₂×C₉	—	3	2	no	—
20	C₂×C₉	C₃×D₃	1	1	yes	characteristic
21	C₂²×C₃	—	3	1	no	—
22	C₂×D₃	C₂₇	1	1	yes	characteristic, direct product factor
23	C₃²	C₂²×C₉	1	1	yes	characteristic
24	C₉	—	2	1	no	—
25	C₉	C₂×C₃×D₃	1	1	yes	characteristic
26	C₂×C₃	—	2	1	no	—
27	C₂×C₃	—	3	2	no	—
28	C₂×C₃	C₂×C₂₇	1	1	yes	characteristic, complemented
29	C₂×C₃	D₃×C₉	1	1	yes	characteristic
30	D₃	C₂×C₂₇	1	2	yes	direct product factor
31	C₂²	—	3	1	no	Sylow
32	C₃	—	2	1	no	—
33	C₃	C₂²×C₂₇	1	1	yes	characteristic, complemented
34	C₃	C₂×D₃×C₉	1	1	yes	characteristic
35	C₂	—	3	2	no	—
36	C₂	D₃×C₂₇	1	1	yes	characteristic, direct product factor

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.