Subgroups — (C₂₇⋊C₃)⋊C₄ #66320

Order 324.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₇⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₉	—	3	1	no	maximal
3	Dic₂₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂₇⋊C₃	C₄	1	1	yes	characteristic, complemented, Sylow
5	C₂×C₃×C₉	D₃	1	1	yes	characteristic
6	C₂×C₂₇	—	2	1	no	—
7	C₂×C₂₇	C₂×C₃	1	1	yes	characteristic
8	C₃×Dic₃	—	9	1	no	—
9	Dic₉	—	3	1	no	—
10	C₃×C₉	Dic₃	1	1	yes	characteristic
11	C₂₇	—	2	1	no	—
12	C₂₇	C₃×C₄	1	1	yes	characteristic, complemented
13	C₂×C₃²	D₉	1	1	yes	characteristic
14	C₂×C₉	—	2	1	no	—
15	C₂×C₉	C₃×D₃	1	1	yes	characteristic
16	C₃×C₄	—	27	1	no	—
17	Dic₃	—	9	1	no	—
18	C₃²	Dic₉	1	1	yes	characteristic
19	C₉	—	2	1	no	—
20	C₉	C₃×Dic₃	1	1	yes	characteristic
21	C₂×C₃	—	3	1	no	—
22	C₂×C₃	C₃×D₉	1	1	yes	characteristic
23	C₄	—	27	1	no	Sylow
24	C₃	—	3	1	no	—
25	C₃	C₃×Dic₉	1	1	yes	characteristic
26	C₂	D₂₇⋊C₃	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.