Subgroups — D₄×C₂₇ #6173

Order 216.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₇	C₂	1	2	yes	maximal, complemented
2	C₄×C₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₉	C₃	1	1	yes	maximal, characteristic
4	C₂×C₂₇	—	2	2	no	—
5	C₂×C₂₇	C₂²	1	1	yes	characteristic
6	C₂²×C₉	C₂×C₃	1	2	yes	—
7	C₄×C₉	C₂×C₃	1	1	yes	characteristic
8	C₂₇	D₄	1	1	yes	characteristic, direct product factor, Sylow
9	C₃×D₄	C₉	1	1	yes	characteristic
10	C₂×C₉	—	2	2	no	—
11	C₂×C₉	C₂²×C₃	1	1	yes	characteristic
12	C₂²×C₃	C₂×C₉	1	2	yes	—
13	C₃×C₄	C₂×C₉	1	1	yes	characteristic
14	C₉	C₃×D₄	1	1	yes	characteristic
15	D₄	C₂₇	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₃	—	2	2	no	—
17	C₂×C₃	C₂²×C₉	1	1	yes	characteristic
18	C₂²	C₂×C₂₇	1	2	yes	complemented
19	C₄	C₂×C₂₇	1	1	yes	characteristic, complemented
20	C₃	D₄×C₉	1	1	yes	characteristic
21	C₂	—	2	2	no	—
22	C₂	C₂²×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.