Subgroups — #22627034

Order 9344.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989669	C₂	1	2	yes	maximal, complemented
2	#17989518	C₂	1	1	yes	maximal, characteristic
3	#14556641	C₄	1	1	yes	characteristic
4	#14556641	C₂²	1	1	yes	characteristic
5	C₁₆×D₇₃	C₄	1	1	yes	characteristic
6	C₈×D₇₃	C₈	1	1	yes	characteristic
7	#11924003	C₂×C₄	1	1	yes	characteristic
8	C₁₆×C₇₃	C₈	1	1	yes	characteristic
9	C₄×D₇₃	C₁₆	1	1	yes	characteristic
10	C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
11	#10596831	C₁₆	1	1	yes	characteristic
12	C₂×D₇₃	C₃₂	1	1	yes	characteristic
13	C₄×C₇₃	C₂×C₁₆	1	1	yes	characteristic
14	Dic₇₃	C₃₂	1	1	yes	characteristic
15	C₂×C₇₃	C₂×C₃₂	1	1	yes	characteristic
16	D₇₃	C₆₄	1	2	yes	complemented
17	C₂×C₆₄	—	73	1	no	maximal, Sylow
18	C₇₃	C₂×C₆₄	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃₂	—	73	1	no	—
20	C₆₄	—	73	2	no	—
21	C₂×C₁₆	—	73	1	no	—
22	C₃₂	—	73	1	no	—
23	C₃₂	—	73	1	no	—
24	C₂×C₈	—	73	1	no	—
25	C₁₆	—	73	1	no	—
26	C₁₆	#10596842	1	1	yes	characteristic
27	C₂×C₄	—	73	1	no	—
28	C₈	—	73	1	no	—
29	C₈	C₂×#10596842	1	1	yes	characteristic
30	C₂²	—	73	1	no	—
31	C₄	—	73	1	no	—
32	C₄	#14556686	1	1	yes	characteristic
33	C₂	—	73	2	no	—
34	C₂	#17989694	1	1	yes	characteristic

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