Subgroups — #36378885

Order 22592.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26015088	C₂	1	2	yes	maximal, complemented
2	C₂×#19150746	C₂	1	1	yes	maximal, characteristic
3	#19150749	—	2	2	no	—
4	#19150746	—	2	2	no	—
5	C₂×#15667732	C₄	1	1	yes	characteristic
6	C₂×#15667732	C₂²	1	1	yes	characteristic
7	C₂²×Dic₃₅₃	C₄	1	1	yes	characteristic
8	#15667732	—	2	1	no	—
9	#15667732	D₄	1	2	yes	—
10	C₂×Dic₃₅₃	—	2	1	no	—
11	C₂×Dic₃₅₃	—	2	1	no	—
12	C₂×Dic₃₅₃	C₈	1	1	yes	characteristic
13	C₂×Dic₃₅₃	C₂×C₄	1	1	yes	characteristic
14	C₂³×C₃₅₃	C₈	1	1	yes	characteristic
15	C₂²×C₃₅₃	—	2	1	no	—
16	C₂²×C₃₅₃	—	4	1	no	—
17	C₂²×C₃₅₃	C₂×C₈	1	1	yes	characteristic
18	Dic₃₅₃	—	2	1	no	—
19	Dic₃₅₃	C₂²⋊C₄	1	1	yes	characteristic
20	Dic₃₅₃	M₁₆	1	1	yes	characteristic
21	C₂×C₃₅₃	—	2	1	no	—
22	C₂×C₃₅₃	—	4	1	no	—
23	C₂×C₃₅₃	C₂²⋊C₈	1	1	yes	characteristic
24	C₃₅₃	#349	1	1	yes	characteristic, complemented, Sylow
25	#349	—	353	1	no	maximal, Sylow
26	C₂×M₁₆	—	353	1	no	—
27	M₃₂	—	353	2	no	—
28	C₂²×C₄	—	353	1	no	—
29	M₁₆	—	706	2	no	—
30	C₂×C₈	—	353	1	no	—
31	C₂×C₈	—	353	1	no	—
32	C₁₆	—	706	2	no	—
33	C₂³	#15667734	1	1	yes	characteristic
34	C₂×C₄	—	353	1	no	—
35	C₂×C₄	—	353	1	no	—
36	C₂×C₄	—	706	1	no	—
37	C₂×C₄	—	706	1	no	—
38	C₈	—	353	2	no	—
39	C₈	—	706	1	no	—
40	C₂²	—	2	1	no	—
41	C₂²	—	4	1	no	—
42	C₂²	C₂×#15667734	1	1	yes	characteristic
43	C₄	—	353	1	no	—
44	C₄	—	353	1	no	—
45	C₄	—	706	1	no	—
46	C₂	—	2	1	no	—
47	C₂	—	4	1	no	—
48	C₂	C₂²⋊#15667734	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #26015088	C₂	semidirect
24. C₃₅₃	#349	semidirect

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