Subgroups — C₂×C₂²⋊C₂₇ #6185

Order 216.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²⋊C₂₇	C₂	1	1	yes	maximal, characteristic, direct product factor
2	C₂³×C₉	C₃	1	1	yes	maximal, characteristic
3	C₂×C₂₇	—	4	1	no	maximal
4	C₂²×C₉	—	3	1	no	—
5	C₂²×C₉	—	3	1	no	—
6	C₂²×C₉	C₂×C₃	1	1	yes	characteristic
7	C₂₇	—	4	1	no	Sylow
8	C₂³×C₃	C₉	1	1	yes	characteristic
9	C₂×C₉	—	3	1	no	—
10	C₂×C₉	—	3	1	no	—
11	C₂×C₉	A₄	1	1	yes	characteristic
12	C₂²×C₃	—	3	1	no	—
13	C₂²×C₃	—	3	1	no	—
14	C₂²×C₃	C₂×C₉	1	1	yes	characteristic
15	C₉	C₂×A₄	1	1	yes	characteristic
16	C₂³	C₂₇	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₃	—	3	1	no	—
18	C₂×C₃	—	3	1	no	—
19	C₂×C₃	C₂²⋊C₉	1	1	yes	characteristic
20	C₂²	—	3	1	no	—
21	C₂²	—	3	1	no	—
22	C₂²	C₂×C₂₇	1	1	yes	characteristic, complemented
23	C₃	C₂×C₂²⋊C₉	1	1	yes	characteristic
24	C₂	—	3	1	no	—
25	C₂	—	3	1	no	—
26	C₂	C₂²⋊C₂₇	1	1	yes	characteristic, direct product factor

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.