Subgroups — #36378718

Order 22592.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26015042	C₂	1	2	yes	maximal, complemented
2	C₁₆×D₃₅₃	C₂	1	1	yes	maximal, characteristic
3	C₈×D₃₅₃	C₄	1	1	yes	characteristic
4	#19150712	C₂²	1	1	yes	characteristic
5	C₁₆×C₃₅₃	C₄	1	1	yes	characteristic
6	C₄×D₃₅₃	C₈	1	1	yes	characteristic
7	#15667725	C₈	1	1	yes	characteristic
8	C₈×C₃₅₃	C₂×C₄	1	1	yes	characteristic
9	C₂×D₃₅₃	C₁₆	1	1	yes	characteristic
10	C₄×C₃₅₃	C₂×C₈	1	1	yes	characteristic
11	Dic₃₅₃	C₁₆	1	1	yes	characteristic
12	C₂×C₃₅₃	C₂×C₁₆	1	1	yes	characteristic
13	D₃₅₃	C₃₂	1	2	yes	complemented
14	C₃₅₃	C₂×C₃₂	1	1	yes	characteristic, complemented, Sylow
15	C₂×C₃₂	—	353	1	no	maximal, Sylow
16	C₂×C₁₆	—	353	1	no	—
17	C₃₂	—	353	2	no	—
18	C₂×C₈	—	353	1	no	—
19	C₁₆	—	353	1	no	—
20	C₁₆	#13083443	1	1	yes	characteristic
21	C₂×C₄	—	353	1	no	—
22	C₈	—	353	1	no	—
23	C₈	C₂×#13083443	1	1	yes	characteristic
24	C₂²	—	353	1	no	—
25	C₄	—	353	1	no	—
26	C₄	#19150745	1	1	yes	characteristic
27	C₂	—	353	2	no	—
28	C₂	#26015065	1	1	yes	characteristic

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.