Subgroups — #22625100

Order 9344.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989426	C₂	1	2	yes	maximal, complemented
2	C₂×#14556497	C₂	1	1	yes	maximal, characteristic
3	#14556497	C₄	1	1	yes	characteristic
4	#14556497	C₂²	1	1	yes	characteristic
5	C₂×C₁₆×C₇₃	C₄	1	1	yes	characteristic
6	C₂×C₈×C₇₃	C₈	1	1	yes	characteristic
7	C₁₆×C₇₃	C₈	1	1	yes	characteristic
8	C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
9	C₂×C₄×C₇₃	C₁₆	1	1	yes	characteristic
10	C₈×C₇₃	C₁₆	1	1	yes	characteristic
11	C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
12	C₂²×C₇₃	C₃₂	1	1	yes	characteristic
13	C₄×C₇₃	C₃₂	1	1	yes	characteristic
14	C₄×C₇₃	C₂×C₁₆	1	1	yes	characteristic
15	C₂×C₇₃	—	2	1	no	—
16	C₂×C₇₃	C₂×C₃₂	1	1	yes	characteristic
17	M₁₂₈	—	73	1	no	maximal, Sylow
18	C₇₃	M₁₂₈	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃₂	—	73	1	no	—
20	C₆₄	—	73	2	no	—
21	C₂×C₁₆	#64408	1	1	yes	characteristic
22	C₃₂	—	73	1	no	—
23	C₃₂	—	73	1	no	—
24	C₂×C₈	#10596833	1	1	yes	characteristic
25	C₁₆	#10596833	1	1	yes	characteristic
26	C₁₆	C₂×#64408	1	1	yes	characteristic
27	C₂×C₄	#11924031	1	1	yes	characteristic
28	C₈	#11924031	1	1	yes	characteristic
29	C₈	C₂×#10596833	1	1	yes	characteristic
30	C₂²	#14556641	1	1	yes	characteristic
31	C₄	#14556641	1	1	yes	characteristic
32	C₄	C₂×#11924031	1	1	yes	characteristic
33	C₂	—	2	1	no	—
34	C₂	C₂×#14556641	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #17989426	C₂	semidirect
18. C₇₃	M₁₂₈	semidirect