Subgroups — C₂²×C₃×C₂₇ #66392

Order 324.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₂₇	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₉	C₃	1	1	yes	maximal, characteristic
3	C₂²×C₂₇	C₃	1	3	yes	maximal, direct product factor
4	C₃×C₂₇	C₂²	1	1	yes	characteristic, direct product factor, Sylow
5	C₂×C₃×C₉	C₂×C₃	1	3	yes	—
6	C₂×C₂₇	C₂×C₃	1	9	yes	direct product factor
7	C₂²×C₃²	C₉	1	1	yes	characteristic
8	C₂²×C₉	C₉	1	2	yes	—
9	C₂²×C₉	C₃²	1	1	yes	characteristic
10	C₃×C₉	C₂²×C₃	1	1	yes	characteristic
11	C₂₇	C₂²×C₃	1	3	yes	direct product factor
12	C₂×C₃²	C₂×C₉	1	3	yes	—
13	C₂×C₉	C₂×C₉	1	6	yes	—
14	C₂×C₉	C₂×C₃²	1	3	yes	—
15	C₂²×C₃	C₂₇	1	3	yes	direct product factor
16	C₂²×C₃	C₃×C₉	1	1	yes	characteristic
17	C₃²	C₂²×C₉	1	1	yes	characteristic
18	C₉	C₂²×C₉	1	2	yes	—
19	C₉	C₂²×C₃²	1	1	yes	characteristic
20	C₂×C₃	C₂×C₂₇	1	9	yes	direct product factor
21	C₂×C₃	C₂×C₃×C₉	1	3	yes	—
22	C₂²	C₃×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
23	C₃	C₂²×C₂₇	1	3	yes	direct product factor
24	C₃	C₂²×C₃×C₉	1	1	yes	characteristic
25	C₂	C₂×C₃×C₂₇	1	3	yes	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.