Subgroups — C₄×C₂₇ #1075

Order 108.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₇	C₂	1	1	yes	maximal, characteristic
2	C₄×C₉	C₃	1	1	yes	maximal, characteristic
3	C₂₇	C₄	1	1	yes	characteristic, direct product factor, Sylow
4	C₂×C₉	C₂×C₃	1	1	yes	characteristic
5	C₃×C₄	C₉	1	1	yes	characteristic
6	C₉	C₃×C₄	1	1	yes	characteristic
7	C₂×C₃	C₂×C₉	1	1	yes	characteristic
8	C₄	C₂₇	1	1	yes	characteristic, direct product factor, Sylow
9	C₃	C₄×C₉	1	1	yes	characteristic
10	C₂	C₂×C₂₇	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₂₇	C₄	direct (N × H)
8. C₄	C₂₇	direct (N × H)

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₂₇	2
C₄×C₉	3