Subgroups — #22608133

Order 9344.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17988413	C₂	1	2	yes	maximal
2	C₂×C₃₂×C₇₃	C₂	1	1	yes	maximal, characteristic
3	#14556525	—	2	2	no	—
4	C₂×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
5	C₃₂×C₇₃	C₄	1	2	yes	complemented
6	C₄⋊Dic₇₃	—	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	C₂×Dic₇₃	—	8	2	no	—
12	C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
13	C₈×C₇₃	Q₁₆	1	1	yes	characteristic
14	C₂²×C₇₃	D₁₆	1	1	yes	characteristic
15	C₄×C₇₃	#107	1	1	yes	characteristic
16	C₄×C₇₃	Q₃₂	1	1	yes	characteristic
17	Dic₇₃	—	16	2	no	—
18	C₂×C₇₃	#366	1	1	yes	characteristic
19	C₂×C₇₃	SD₆₄	1	2	yes	—
20	#1424	—	73	1	no	maximal, Sylow
21	C₇₃	#1424	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₃₂	D₇₃	1	1	yes	characteristic
23	#366	—	73	2	no	—
24	C₂×C₁₆	C₂×D₇₃	1	1	yes	characteristic
25	#107	—	146	2	no	—
26	C₃₂	Dic₇₃	1	2	yes	complemented
27	C₂×C₈	D₂₉₂	1	1	yes	characteristic
28	C₄⋊C₄	—	292	2	no	—
29	C₁₆	Dic₁₄₆	1	1	yes	characteristic
30	C₁₆	C₂×Dic₇₃	1	1	yes	characteristic
31	C₂×C₄	—	584	2	no	—
32	C₂×C₄	D₅₈₄	1	1	yes	characteristic
33	C₈	C₄⋊Dic₇₃	1	1	yes	characteristic
34	C₈	Dic₂₉₂	1	1	yes	characteristic
35	C₂²	D₁₁₆₈	1	1	yes	characteristic
36	C₄	—	1168	2	no	—
37	C₄	#14556525	1	1	yes	characteristic
38	C₄	Dic₅₈₄	1	1	yes	characteristic
39	C₂	#17988413	1	1	yes	characteristic
40	C₂	#17988426	1	2	yes	—

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