Subgroups — #126⋊C₂₇ #11720113

Order 864.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²⋊C₂₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#126	C₃	1	1	yes	maximal, characteristic
3	C₂×C₂²⋊C₂₇	—	4	1	no	maximal
4	C₉×C₄⋊C₄	—	3	1	no	—
5	C₉×C₂²⋊C₄	—	3	1	no	—
6	C₄²×C₉	C₂×C₃	1	1	yes	characteristic
7	C₂²⋊C₂₇	—	4	1	no	—
8	C₃×#126	C₉	1	1	yes	characteristic
9	C₂³×C₉	A₄	1	1	yes	characteristic
10	C₂×C₄×C₉	—	3	1	no	—
11	C₂×C₄×C₉	—	3	1	no	—
12	C₂×C₂₇	—	16	1	no	—
13	C₃×C₄⋊C₄	—	3	1	no	—
14	C₃×C₂²⋊C₄	—	3	1	no	—
15	C₃×C₄²	C₂×C₉	1	1	yes	characteristic
16	C₂²×C₉	—	6	1	no	—
17	C₂²×C₉	C₂×A₄	1	1	yes	characteristic
18	C₄×C₉	—	6	1	no	—
19	C₄×C₉	—	6	1	no	—
20	#126	C₂₇	1	1	yes	characteristic, complemented, Sylow
21	C₂₇	—	16	1	no	Sylow
22	C₂³×C₃	C₂²⋊C₉	1	1	yes	characteristic
23	C₂×C₃×C₄	—	3	1	no	—
24	C₂×C₃×C₄	—	3	1	no	—
25	C₂×C₉	—	3	1	no	—
26	C₂×C₉	—	4	1	no	—
27	C₄⋊C₄	—	3	1	no	—
28	C₂²⋊C₄	—	3	1	no	—
29	C₄²	C₂×C₂₇	1	1	yes	characteristic, complemented
30	C₂²×C₃	—	6	1	no	—
31	C₂²×C₃	C₂×C₂²⋊C₉	1	1	yes	characteristic
32	C₃×C₄	—	6	1	no	—
33	C₃×C₄	—	6	1	no	—
34	C₉	#126⋊C₃	1	1	yes	characteristic
35	C₂³	C₂²⋊C₂₇	1	1	yes	characteristic
36	C₂×C₄	—	3	1	no	—
37	C₂×C₄	—	3	1	no	—
38	C₂×C₃	—	3	1	no	—
39	C₂×C₃	—	4	1	no	—
40	C₂²	—	6	1	no	—
41	C₂²	C₂×C₂²⋊C₂₇	1	1	yes	characteristic
42	C₄	—	6	1	no	—
43	C₄	—	6	1	no	—
44	C₃	#126⋊C₉	1	1	yes	characteristic
45	C₂	—	3	1	no	—
46	C₂	—	4	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.