Subgroups — #22625092

Order 9344.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989513	C₂	1	2	yes	maximal
2	C₃₂×D₇₃	C₂	1	1	yes	maximal, characteristic
3	#14556660	—	2	2	no	—
4	C₁₆×D₇₃	C₂²	1	1	yes	characteristic
5	#14556497	C₄	1	1	yes	characteristic, complemented
6	C₃₂×C₇₃	C₄	1	1	yes	characteristic, complemented
7	C₄⋊#64408	—	4	2	no	—
8	C₈×D₇₃	D₄	1	1	yes	characteristic
9	#11924003	Q₈	1	1	yes	characteristic
10	C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
11	C₂×#64408	—	8	2	no	—
12	C₄×D₇₃	D₈	1	1	yes	characteristic
13	C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
14	#10596831	Q₁₆	1	1	yes	characteristic
15	C₂×D₇₃	D₁₆	1	1	yes	characteristic
16	#64408	—	16	2	no	—
17	C₄×C₇₃	#107	1	1	yes	characteristic
18	Dic₇₃	Q₃₂	1	1	yes	characteristic
19	C₂×C₇₃	#366	1	1	yes	characteristic
20	D₇₃	D₃₂	1	1	yes	characteristic
21	D₇₃	Q₆₄	1	1	yes	characteristic
22	#1423	—	73	1	no	maximal, Sylow
23	C₇₃	#1423	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₃₂	—	73	1	no	—
25	#366	—	73	2	no	—
26	C₂×C₁₆	—	73	1	no	—
27	#107	—	146	2	no	—
28	C₃₂	—	73	1	no	—
29	C₃₂	#64408	1	1	yes	characteristic, complemented
30	C₂×C₈	—	73	1	no	—
31	C₄⋊C₄	—	292	2	no	—
32	C₁₆	—	73	1	no	—
33	C₁₆	C₂×#64408	1	1	yes	characteristic
34	C₂×C₄	—	584	2	no	—
35	C₂×C₄	—	73	1	no	—
36	C₈	—	73	1	no	—
37	C₈	C₄⋊#64408	1	1	yes	characteristic
38	C₂²	—	73	1	no	—
39	C₄	—	73	1	no	—
40	C₄	—	1168	2	no	—
41	C₄	#14556660	1	1	yes	characteristic
42	C₂	—	73	1	no	—
43	C₂	—	73	1	no	—
44	C₂	#17989513	1	1	yes	characteristic

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