Subgroups — D₁₀₈ #6169

Order 216.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₇	C₂	1	2	yes	maximal, complemented
2	C₄×C₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃₆	—	3	1	no	maximal
4	C₂×C₂₇	C₂²	1	1	yes	characteristic
5	D₂₇	—	2	2	no	—
6	C₂×D₉	—	3	2	no	—
7	C₄×C₉	D₃	1	1	yes	characteristic
8	C₂₇	D₄	1	1	yes	characteristic, complemented, Sylow
9	D₁₂	—	9	1	no	—
10	C₂×C₉	C₂×D₃	1	1	yes	characteristic
11	D₉	—	6	2	no	—
12	C₂×D₃	—	9	2	no	—
13	C₃×C₄	D₉	1	1	yes	characteristic
14	C₉	D₁₂	1	1	yes	characteristic
15	D₄	—	27	1	no	Sylow
16	C₂×C₃	C₂×D₉	1	1	yes	characteristic
17	D₃	—	18	2	no	—
18	C₂²	—	27	2	no	—
19	C₄	D₂₇	1	1	yes	characteristic, complemented
20	C₃	D₃₆	1	1	yes	characteristic
21	C₂	—	54	2	no	—
22	C₂	C₂×D₂₇	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.