Subgroups — #35232593

Order 21152.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24902381	C₂	1	2	yes	maximal, complemented
2	C₂×C₂²⋊D₆₆₁	C₂	1	1	yes	maximal, characteristic
3	#19126978	—	2	2	no	—
4	C₂²×D₆₆₁	C₄	1	1	yes	characteristic
5	C₂²⋊D₆₆₁	—	2	2	no	—
6	C₂×Dic₆₆₁	C₂²	1	1	yes	characteristic
7	C₂³×C₆₆₁	C₄	1	1	yes	characteristic
8	C₂²×C₆₆₁	—	2	1	no	—
9	C₂²×C₆₆₁	—	4	1	no	—
10	C₂²×C₆₆₁	C₂×C₄	1	1	yes	characteristic
11	C₂×D₆₆₁	—	2	1	no	—
12	C₂×D₆₆₁	—	4	1	no	—
13	Dic₆₆₁	D₄	1	2	yes	—
14	C₂×C₆₆₁	—	2	1	no	—
15	C₂×C₆₆₁	—	4	1	no	—
16	C₂×C₆₆₁	C₂²⋊C₄	1	1	yes	characteristic
17	D₆₆₁	—	4	1	no	—
18	C₆₆₁	#100	1	1	yes	characteristic, complemented, Sylow
19	#100	—	661	1	no	maximal, Sylow
20	C₂×D₄	—	661	1	no	—
21	M₁₆	—	661	2	no	—
22	C₂³	—	661	1	no	—
23	C₂³	#14581558	1	1	yes	characteristic
24	D₄	—	1322	2	no	—
25	C₂×C₄	—	661	1	no	—
26	C₈	—	1322	2	no	—
27	C₂²	—	2	1	no	—
28	C₂²	—	4	1	no	—
29	C₂²	—	1322	1	no	—
30	C₂²	—	2644	1	no	—
31	C₂²	C₂×#14581558	1	1	yes	characteristic
32	C₄	—	661	2	no	—
33	C₂	—	2	1	no	—
34	C₂	—	4	1	no	—
35	C₂	—	2644	1	no	—
36	C₂	C₂²⋊#14581558	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #24902381	C₂	semidirect
18. C₆₆₁	#100	semidirect

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