Subgroups — C₂₇×C₂²⋊A₄ #13048164

Order 1296.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₂²⋊A₄	C₃	1	1	yes	maximal, characteristic
2	C₂⁴×C₂₇	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊(C₂²⋊C₂₇)	C₃	1	2	yes	maximal, complemented
4	A₄×C₂₇	—	4	5	no	maximal
5	C₂³×C₂₇	—	3	5	no	—
6	C₃×C₂²⋊A₄	C₉	1	1	yes	characteristic
7	C₂⁴×C₉	C₃²	1	1	yes	characteristic
8	C₂²⋊(C₂²⋊C₉)	C₉	1	2	yes	—
9	C₉×A₄	—	4	5	no	—
10	C₂²×C₂₇	—	3	10	no	—
11	C₂²×C₂₇	A₄	1	5	yes	complemented
12	C₂²⋊C₂₇	—	4	10	no	—
13	C₃×C₂₇	—	16	1	no	Sylow
14	C₂³×C₉	—	3	5	no	—
15	C₂×C₂₇	—	3	5	no	—
16	C₂⁴×C₃	C₃×C₉	1	1	yes	characteristic
17	C₂²⋊A₄	C₂₇	1	3	yes	direct product factor
18	C₃×A₄	—	4	5	no	—
19	C₂²×C₉	—	3	10	no	—
20	C₂²×C₉	C₃×A₄	1	5	yes	—
21	C₂²⋊C₉	—	4	10	no	—
22	C₃×C₉	—	16	1	no	—
23	C₂₇	—	16	2	no	—
24	C₂₇	C₂²⋊A₄	1	1	yes	characteristic, direct product factor
25	C₂³×C₃	—	3	5	no	—
26	C₂×C₉	—	3	5	no	—
27	C₂⁴	C₃×C₂₇	1	1	yes	characteristic, complemented, Sylow
28	C₂²×C₃	—	3	10	no	—
29	C₂²×C₃	C₉×A₄	1	5	yes	—
30	A₄	—	4	15	no	—
31	C₃²	—	16	1	no	—
32	C₉	—	16	2	no	—
33	C₉	C₃×C₂²⋊A₄	1	1	yes	characteristic
34	C₂³	—	3	5	no	—
35	C₂×C₃	—	3	5	no	—
36	C₂²	—	3	10	no	—
37	C₂²	A₄×C₂₇	1	5	yes	complemented
38	C₃	—	16	3	no	—
39	C₃	C₉×C₂²⋊A₄	1	1	yes	characteristic
40	C₂	—	3	5	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.