Subgroups — #36378679

Order 22592.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26015066	C₂	1	2	yes	maximal
2	#26014903	C₂	1	1	yes	maximal, characteristic
3	#19150740	C₄	1	4	yes	complemented
4	C₂×#15667725	C₄	1	1	yes	characteristic
5	C₂×#15667725	C₂²	1	1	yes	characteristic
6	C₄²×C₃₅₃	C₄	1	1	yes	characteristic
7	#15667725	—	2	1	no	—
8	#15667725	C₂×C₄	1	2	yes	—
9	C₂×C₄×C₃₅₃	—	2	1	no	—
10	C₂×C₄×C₃₅₃	C₂×C₄	1	1	yes	characteristic
11	C₂²×C₃₅₃	M₁₆	1	1	yes	characteristic
12	C₄×C₃₅₃	—	4	1	no	—
13	C₄×C₃₅₃	C₄²	1	1	yes	characteristic
14	C₄×C₃₅₃	M₁₆	1	1	yes	characteristic
15	C₂×C₃₅₃	—	2	1	no	—
16	C₂×C₃₅₃	#97	1	1	yes	characteristic
17	C₃₅₃	#347	1	1	yes	characteristic, complemented, Sylow
18	#347	—	353	1	no	maximal, Sylow
19	M₃₂	—	353	2	no	—
20	#97	—	353	1	no	—
21	C₂×C₈	—	353	1	no	—
22	C₂×C₈	—	353	1	no	—
23	C₄²	#13083443	1	1	yes	characteristic
24	C₁₆	—	353	4	no	—
25	C₂×C₄	—	2	1	no	—
26	C₂×C₄	C₂×#13083443	1	1	yes	characteristic
27	C₈	—	353	2	no	—
28	C₈	—	706	1	no	—
29	C₂²	#19150746	1	1	yes	characteristic
30	C₄	—	4	1	no	—
31	C₄	C₄×#13083443	1	1	yes	characteristic
32	C₄	#19150747	1	1	yes	characteristic
33	C₂	—	2	1	no	—
34	C₂	#26015047	1	1	yes	characteristic

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

N	H ≅ G/N	type
3. #19150740	C₄	semidirect
17. C₃₅₃	#347	semidirect

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