Subgroups — #22608135

Order 9344.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17988417	C₂	1	2	yes	maximal
2	C₂×C₃₂×C₇₃	C₂	1	1	yes	maximal, characteristic
3	#14556527	—	2	2	no	—
4	C₂×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
5	C₃₂×C₇₃	C₄	1	2	yes	—
6	#11924012	—	4	2	no	—
7	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
8	C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
9	C₁₆×C₇₃	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₇₃	D₈	1	1	yes	characteristic
11	C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
12	C₈×C₇₃	Q₁₆	1	1	yes	characteristic
13	#10596831	—	8	2	no	—
14	C₂²×C₇₃	Q₃₂	1	1	yes	characteristic
15	C₄×C₇₃	#107	1	1	yes	characteristic
16	C₄×C₇₃	D₁₆	1	1	yes	characteristic
17	C₂×C₇₃	—	2	1	no	—
18	C₂×C₇₃	#366	1	1	yes	characteristic
19	#1425	—	73	1	no	maximal, Sylow
20	C₇₃	#1425	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₃₂	D₇₃	1	1	yes	characteristic
22	#368	—	73	2	no	—
23	C₂×C₁₆	C₂×D₇₃	1	1	yes	characteristic
24	#108	—	146	2	no	—
25	C₃₂	Dic₇₃	1	2	yes	—
26	M₁₆	—	292	2	no	—
27	C₂×C₈	D₂₉₂	1	1	yes	characteristic
28	C₁₆	Dic₁₄₆	1	1	yes	characteristic
29	C₁₆	C₂×Dic₇₃	1	1	yes	characteristic
30	C₂×C₄	D₅₈₄	1	1	yes	characteristic
31	C₈	—	584	2	no	—
32	C₈	C₄⋊Dic₇₃	1	1	yes	characteristic
33	C₈	Dic₂₉₂	1	1	yes	characteristic
34	C₂²	Dic₅₈₄	1	1	yes	characteristic
35	C₄	#14556525	1	1	yes	characteristic
36	C₄	D₁₁₆₈	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#17988413	1	1	yes	characteristic

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

N	H ≅ G/N	type
20. C₇₃	#1425	semidirect