Subgroups — C₃×C₂²⋊C₈₁ #11757421

Order 972.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₂₇	C₃	1	1	yes	maximal, characteristic
2	C₂²⋊C₈₁	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₈₁	—	4	1	no	maximal, Sylow
4	C₂×C₃×C₂₇	—	3	1	no	—
5	C₂²×C₃×C₉	C₉	1	1	yes	characteristic
6	C₂²×C₂₇	C₉	1	2	yes	—
7	C₂²×C₂₇	C₃²	1	1	yes	characteristic
8	C₃×C₂₇	A₄	1	1	yes	characteristic
9	C₈₁	—	4	3	no	—
10	C₂×C₃×C₉	—	3	1	no	—
11	C₂×C₂₇	—	3	2	no	—
12	C₂×C₂₇	—	3	1	no	—
13	C₂²×C₃²	C₂₇	1	1	yes	characteristic
14	C₂²×C₉	C₂₇	1	2	yes	—
15	C₂²×C₉	C₃×C₉	1	1	yes	characteristic
16	C₃×C₉	C₂²⋊C₉	1	1	yes	characteristic
17	C₂₇	C₂²⋊C₉	1	2	yes	—
18	C₂₇	C₃×A₄	1	1	yes	characteristic
19	C₂×C₃²	—	3	1	no	—
20	C₂×C₉	—	3	2	no	—
21	C₂×C₉	—	3	1	no	—
22	C₂²×C₃	C₈₁	1	3	yes	complemented
23	C₂²×C₃	C₃×C₂₇	1	1	yes	characteristic
24	C₃²	C₂²⋊C₂₇	1	1	yes	characteristic
25	C₉	C₂²⋊C₂₇	1	2	yes	—
26	C₉	C₃×C₂²⋊C₉	1	1	yes	characteristic
27	C₂×C₃	—	3	3	no	—
28	C₂×C₃	—	3	1	no	—
29	C₂²	C₃×C₈₁	1	1	yes	characteristic, complemented, Sylow
30	C₃	C₂²⋊C₈₁	1	3	yes	direct product factor
31	C₃	C₃×C₂²⋊C₂₇	1	1	yes	characteristic
32	C₂	—	3	1	no	—

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.