Subgroups — C₇₃×#1308 #22605461

Order 9344.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#432×C₇₃	C₂	1	3	yes	maximal
2	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
3	C₄⋊C₈×C₇₃	—	2	3	no	—
4	C₂²⋊C₈×C₇₃	C₄	1	6	yes	—
5	#97×C₇₃	—	2	3	no	—
6	C₂²×C₄×C₇₃	C₂×C₄	1	3	yes	—
7	C₂×C₈×C₇₃	—	2	6	no	—
8	C₄²×C₇₃	D₄	1	3	yes	—
9	C₄²×C₇₃	Q₈	1	1	yes	characteristic
10	C₂³×C₇₃	C₄²	1	1	yes	characteristic
11	C₂×C₄×C₇₃	—	4	3	no	—
12	C₂×C₄×C₇₃	C₂²⋊C₄	1	3	yes	—
13	C₂×C₄×C₇₃	C₄⋊C₄	1	3	yes	—
14	C₈×C₇₃	—	4	6	no	—
15	C₂²×C₇₃	—	2	3	no	—
16	C₂²×C₇₃	#95	1	1	yes	characteristic
17	C₄×C₇₃	—	2	3	no	—
18	C₄×C₇₃	—	2	3	no	—
19	C₂×C₇₃	—	4	1	no	—
20	C₂×C₇₃	#344	1	3	yes	—
21	#1308	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
22	C₇₃	#1308	1	1	yes	characteristic, direct product factor, Sylow
23	#432	C₂×C₇₃	1	3	yes	—
24	C₂×C₄²	C₂²×C₇₃	1	1	yes	characteristic
25	C₄⋊C₈	—	2	3	no	—
26	C₂²⋊C₈	C₄×C₇₃	1	6	yes	—
27	#97	—	2	3	no	—
28	C₂²×C₄	C₂×C₄×C₇₃	1	3	yes	—
29	C₂×C₈	—	2	6	no	—
30	C₄²	D₄×C₇₃	1	3	yes	—
31	C₄²	Q₈×C₇₃	1	1	yes	characteristic
32	C₂³	C₄²×C₇₃	1	1	yes	characteristic
33	C₂×C₄	—	4	3	no	—
34	C₂×C₄	C₂²⋊C₄×C₇₃	1	3	yes	—
35	C₂×C₄	C₄⋊C₄×C₇₃	1	3	yes	—
36	C₈	—	4	6	no	—
37	C₂²	—	2	3	no	—
38	C₂²	#95×C₇₃	1	1	yes	characteristic
39	C₄	—	2	3	no	—
40	C₄	—	2	3	no	—
41	C₂	—	4	1	no	—
42	C₂	#344×C₇₃	1	3	yes	—

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

N	H ≅ G/N	type
21. #1308	C₇₃	direct (N × H)
22. C₇₃	#1308	direct (N × H)

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#432×C₇₃	2
#1308	73