Subgroups — C₄²⋊C₂₇ #88356

Order 432.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×C₉	C₃	1	1	yes	maximal, characteristic
2	C₂²⋊C₂₇	—	4	1	no	maximal
3	C₂×C₄×C₉	—	3	1	no	—
4	C₃×C₄²	C₉	1	1	yes	characteristic
5	C₂²×C₉	A₄	1	1	yes	characteristic
6	C₄×C₉	—	3	2	no	—
7	C₂₇	—	16	1	no	Sylow
8	C₂×C₃×C₄	—	3	1	no	—
9	C₂×C₉	—	3	1	no	—
10	C₄²	C₂₇	1	1	yes	characteristic, complemented, Sylow
11	C₂²×C₃	C₂²⋊C₉	1	1	yes	characteristic
12	C₃×C₄	—	3	2	no	—
13	C₉	C₄²⋊C₃	1	1	yes	characteristic
14	C₂×C₄	—	3	1	no	—
15	C₂×C₃	—	3	1	no	—
16	C₂²	C₂²⋊C₂₇	1	1	yes	characteristic
17	C₄	—	3	2	no	—
18	C₃	C₄²⋊C₉	1	1	yes	characteristic
19	C₂	—	3	1	no	—

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

N	H ≅ G/N	type
10. C₄²	C₂₇	semidirect

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

subgroup	index
C₄²×C₉	3
C₂²⋊C₂₇	4