Subgroups — #36378678

Order 22592.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26015067	C₂	1	1	yes	maximal, characteristic
2	#26015046	C₂	1	1	yes	maximal, characteristic
3	#26014931	C₂	1	1	yes	maximal, characteristic
4	#19150745	C₄	1	1	yes	characteristic
5	C₄×#13083443	C₄	1	1	yes	characteristic
6	#19150740	C₄	1	2	yes	complemented
7	C₈×D₃₅₃	C₂²	1	1	yes	characteristic
8	#19150712	C₄	1	1	yes	characteristic, complemented
9	C₁₆×C₃₅₃	C₄	1	1	yes	characteristic, complemented
10	C₂×#13083443	—	2	1	no	—
11	#15667732	—	2	1	no	—
12	C₄×D₃₅₃	C₂×C₄	1	1	yes	characteristic
13	#15667725	C₂×C₄	1	1	yes	characteristic
14	C₈×C₃₅₃	C₂×C₄	1	1	yes	characteristic
15	C₂×D₃₅₃	M₁₆	1	1	yes	characteristic
16	#13083443	—	4	1	no	—
17	C₄×C₃₅₃	C₄²	1	1	yes	characteristic
18	Dic₃₅₃	M₁₆	1	1	yes	characteristic
19	C₂×C₃₅₃	#97	1	1	yes	characteristic
20	D₃₅₃	—	2	1	no	—
21	C₃₅₃	#347	1	1	yes	characteristic, complemented, Sylow
22	#347	—	353	1	no	maximal, Sylow
23	M₃₂	—	353	1	no	—
24	M₃₂	—	353	1	no	—
25	#97	—	353	1	no	—
26	C₂×C₈	—	353	1	no	—
27	C₂×C₈	—	353	1	no	—
28	C₄²	—	353	1	no	—
29	C₁₆	—	353	2	no	—
30	C₁₆	—	353	1	no	—
31	C₁₆	#13083443	1	1	yes	characteristic, complemented
32	C₂×C₄	—	353	1	no	—
33	C₂×C₄	—	706	1	no	—
34	C₈	—	353	1	no	—
35	C₈	—	706	1	no	—
36	C₈	C₂×#13083443	1	1	yes	characteristic
37	C₂²	—	353	1	no	—
38	C₄	—	353	1	no	—
39	C₄	—	1412	1	no	—
40	C₄	C₄×#13083443	1	1	yes	characteristic
41	C₂	—	706	1	no	—
42	C₂	#26015046	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.