Subgroups — #22626993

Order 9344.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989691	C₂	1	2	yes	maximal
2	#17989474	C₂	1	1	yes	maximal, characteristic
3	#14556688	—	2	2	no	—
4	#14556664	C₄	1	1	yes	characteristic
5	C₈×#64408	C₂²	1	1	yes	characteristic
6	C₁₆×D₇₃	C₄	1	1	yes	characteristic
7	#11924040	—	4	2	no	—
8	#11924036	D₄	1	1	yes	characteristic
9	C₄×#64408	Q₈	1	1	yes	characteristic
10	#11924031	—	2	1	no	—
11	C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
12	#11924003	C₈	1	1	yes	characteristic
13	C₁₆×C₇₃	C₈	1	1	yes	characteristic
14	C₂×#64408	—	2	1	no	—
15	C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
16	#10596833	SD₁₆	1	2	yes	—
17	C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
18	#10596831	M₁₆	1	1	yes	characteristic
19	C₂×D₇₃	#108	1	1	yes	characteristic
20	#64408	—	4	1	no	—
21	C₄×C₇₃	C₄⋊C₈	1	1	yes	characteristic
22	Dic₇₃	#106	1	1	yes	characteristic
23	C₂×C₇₃	#334	1	1	yes	characteristic
24	D₇₃	—	2	1	no	—
25	#1369	—	73	1	no	maximal, Sylow
26	C₇₃	#1369	1	1	yes	characteristic, complemented, Sylow
27	#364	—	73	2	no	—
28	#346	—	73	1	no	—
29	M₃₂	—	146	2	no	—
30	C₂×C₁₆	—	73	1	no	—
31	C₂×C₁₆	—	73	1	no	—
32	C₄×C₈	—	73	1	no	—
33	C₂×C₈	—	73	1	no	—
34	C₂×C₈	—	73	1	no	—
35	C₄²	—	73	1	no	—
36	C₁₆	—	292	2	no	—
37	C₁₆	—	73	1	no	—
38	C₁₆	—	146	1	no	—
39	C₁₆	#10596842	1	1	yes	characteristic
40	C₂×C₄	—	73	1	no	—
41	C₂×C₄	—	146	1	no	—
42	C₈	—	73	2	no	—
43	C₈	—	73	1	no	—
44	C₈	C₂×#10596842	1	1	yes	characteristic
45	C₂²	—	73	1	no	—
46	C₄	—	292	1	no	—
47	C₄	—	73	1	no	—
48	C₄	C₄⋊#10596842	1	1	yes	characteristic
49	C₂	—	146	1	no	—
50	C₂	#17989676	1	1	yes	characteristic

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

N	H ≅ G/N	type
26. C₇₃	#1369	semidirect