Subgroups — Dic₃×C₂₇ #66319

Order 324.

30 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	C₉×Dic₃	C₃	1	1	yes	maximal, characteristic
3	C₄×C₂₇	—	3	1	no	maximal
4	C₃×C₂₇	C₄	1	1	yes	characteristic, complemented, Sylow
5	C₂×C₃×C₉	C₂×C₃	1	1	yes	characteristic
6	C₂×C₂₇	—	2	1	no	—
7	C₂×C₂₇	D₃	1	1	yes	characteristic
8	C₃×Dic₃	C₉	1	1	yes	characteristic
9	C₄×C₉	—	3	1	no	—
10	C₃×C₉	C₃×C₄	1	1	yes	characteristic
11	C₂₇	—	2	1	no	—
12	C₂₇	Dic₃	1	1	yes	characteristic, direct product factor
13	C₂×C₃²	C₂×C₉	1	1	yes	characteristic
14	C₂×C₉	—	2	1	no	—
15	C₂×C₉	C₃×D₃	1	1	yes	characteristic
16	C₃×C₄	—	3	1	no	—
17	Dic₃	C₂₇	1	1	yes	characteristic, direct product factor
18	C₃²	C₄×C₉	1	1	yes	characteristic
19	C₉	—	2	1	no	—
20	C₉	C₃×Dic₃	1	1	yes	characteristic
21	C₂×C₃	—	2	1	no	—
22	C₂×C₃	C₂×C₂₇	1	1	yes	characteristic
23	C₂×C₃	D₃×C₉	1	1	yes	characteristic
24	C₄	—	3	1	no	Sylow
25	C₃	—	2	1	no	—
26	C₃	C₄×C₂₇	1	1	yes	characteristic, complemented
27	C₃	C₉×Dic₃	1	1	yes	characteristic
28	C₂	D₃×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.