Subgroups — #36377616

Order 22592.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19150712	C₂	1	1	yes	maximal, characteristic
2	#26014928	C₂	1	1	yes	maximal, characteristic
3	#108×C₃₅₃	C₂	1	1	yes	maximal, characteristic
4	#19150721	—	2	1	no	—
5	#19150712	C₄	1	2	yes	—
6	M₁₆×C₃₅₃	—	2	1	no	—
7	C₂×C₈×C₃₅₃	C₂²	1	1	yes	characteristic
8	#15667725	—	4	1	no	—
9	C₂×C₄×C₃₅₃	D₄	1	1	yes	characteristic
10	C₈×C₃₅₃	—	4	1	no	—
11	C₈×C₃₅₃	C₂×C₄	1	1	yes	characteristic
12	C₈×C₃₅₃	Q₈	1	1	yes	characteristic
13	C₂²×C₃₅₃	Q₁₆	1	1	yes	characteristic
14	C₄×C₃₅₃	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₃₅₃	D₈	1	1	yes	characteristic
16	C₂×C₃₅₃	—	2	1	no	—
17	C₂×C₃₅₃	#107	1	1	yes	characteristic
18	C₃₅₃	#368	1	1	yes	characteristic, complemented, Sylow
19	#368	—	353	1	no	maximal, Sylow
20	C₂×C₁₆	—	353	1	no	—
21	#108	—	353	1	no	—
22	#108	D₃₅₃	1	1	yes	characteristic
23	M₁₆	—	2	1	no	—
24	M₁₆	—	706	1	no	—
25	C₂×C₈	C₂×D₃₅₃	1	1	yes	characteristic
26	C₁₆	—	353	2	no	—
27	C₂×C₄	C₂²⋊D₃₅₃	1	1	yes	characteristic
28	C₈	—	4	1	no	—
29	C₈	—	1412	1	no	—
30	C₈	C₄×D₃₅₃	1	1	yes	characteristic
31	C₈	Dic₇₀₆	1	1	yes	characteristic
32	C₂²	#19150727	1	1	yes	characteristic
33	C₄	#19150716	1	1	yes	characteristic
34	C₄	#19150722	1	1	yes	characteristic
35	C₂	—	2	1	no	—
36	C₂	#26014925	1	1	yes	characteristic

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

N	H ≅ G/N	type
18. C₃₅₃	#368	semidirect

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