Subgroups — C₃×C₄×C₂₇ #66337

Order 324.

42 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
2	C₃×C₄×C₉	C₃	1	1	yes	maximal, characteristic
3	C₄×C₂₇	C₃	1	3	yes	maximal, direct product factor
4	C₃×C₂₇	C₄	1	1	yes	characteristic, direct product factor, Sylow
5	C₂×C₃×C₉	C₂×C₃	1	1	yes	characteristic
6	C₂×C₂₇	C₂×C₃	1	3	yes	—
7	C₃²×C₄	C₉	1	1	yes	characteristic
8	C₄×C₉	C₉	1	2	yes	—
9	C₄×C₉	C₃²	1	1	yes	characteristic
10	C₃×C₉	C₃×C₄	1	1	yes	characteristic
11	C₂₇	C₃×C₄	1	3	yes	direct product factor
12	C₂×C₃²	C₂×C₉	1	1	yes	characteristic
13	C₂×C₉	C₂×C₉	1	2	yes	—
14	C₂×C₉	C₂×C₃²	1	1	yes	characteristic
15	C₃×C₄	C₂₇	1	3	yes	direct product factor
16	C₃×C₄	C₃×C₉	1	1	yes	characteristic
17	C₃²	C₄×C₉	1	1	yes	characteristic
18	C₉	C₄×C₉	1	2	yes	—
19	C₉	C₃²×C₄	1	1	yes	characteristic
20	C₂×C₃	C₂×C₂₇	1	3	yes	—
21	C₂×C₃	C₂×C₃×C₉	1	1	yes	characteristic
22	C₄	C₃×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
23	C₃	C₄×C₂₇	1	3	yes	direct product factor
24	C₃	C₃×C₄×C₉	1	1	yes	characteristic
25	C₂	C₂×C₃×C₂₇	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.