Subgroups — #36378881

Order 22592.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19150749	C₂	1	2	yes	maximal
2	C₄×#15667732	C₂	1	1	yes	maximal, characteristic
3	#19150749	C₄	1	4	yes	complemented
4	C₂×#15667732	C₄	1	1	yes	characteristic
5	C₂×#15667732	C₂²	1	1	yes	characteristic
6	C₄×Dic₃₅₃	C₄	1	1	yes	characteristic
7	#15667732	C₈	1	2	yes	—
8	#15667732	C₂×C₄	1	2	yes	—
9	C₂×Dic₃₅₃	C₈	1	1	yes	characteristic
10	C₂×Dic₃₅₃	C₂×C₄	1	1	yes	characteristic
11	C₂×C₄×C₃₅₃	C₈	1	1	yes	characteristic
12	C₂²×C₃₅₃	C₂×C₈	1	1	yes	characteristic
13	C₄×C₃₅₃	—	2	1	no	—
14	Dic₃₅₃	—	2	1	no	—
15	Dic₃₅₃	C₄²	1	1	yes	characteristic
16	Dic₃₅₃	C₂×C₈	1	1	yes	characteristic
17	C₂×C₃₅₃	C₄×C₈	1	1	yes	characteristic
18	C₂×C₃₅₃	M₃₂	1	1	yes	characteristic
19	C₂×C₃₅₃	M₃₂	1	1	yes	characteristic
20	C₃₅₃	#346	1	1	yes	characteristic, complemented, Sylow
21	#346	—	353	1	no	maximal, Sylow
22	C₂×C₁₆	—	353	2	no	—
23	C₄×C₈	—	353	1	no	—
24	C₂×C₈	—	353	1	no	—
25	C₂×C₈	—	353	1	no	—
26	C₄²	—	353	1	no	—
27	C₁₆	—	353	4	no	—
28	C₂×C₄	—	353	1	no	—
29	C₂×C₄	—	353	1	no	—
30	C₂×C₄	#15667734	1	1	yes	characteristic
31	C₈	—	353	2	no	—
32	C₈	—	353	2	no	—
33	C₂²	C₂×#15667734	1	1	yes	characteristic
34	C₄	—	2	1	no	—
35	C₄	—	353	1	no	—
36	C₄	—	353	1	no	—
37	C₄	—	706	1	no	—
38	C₂	C₄×#15667734	1	1	yes	characteristic
39	C₂	#26015088	1	1	yes	characteristic
40	C₂	#26015089	1	1	yes	characteristic

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

N	H ≅ G/N	type
3. #19150749	C₄	semidirect
20. C₃₅₃	#346	semidirect

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