Subgroups — #36368726

Order 22144.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26012419	C₂	1	2	yes	maximal
2	C₃₂×D₁₇₃	C₂	1	1	yes	maximal, characteristic
3	#19149750	—	2	2	no	—
4	C₁₆×D₁₇₃	C₂²	1	1	yes	characteristic
5	#19149585	C₄	1	1	yes	characteristic
6	C₃₂×C₁₇₃	C₄	1	1	yes	characteristic
7	#14583836	—	4	2	no	—
8	C₈×D₁₇₃	D₄	1	1	yes	characteristic
9	#14583801	Q₈	1	1	yes	characteristic
10	C₁₆×C₁₇₃	C₂×C₄	1	1	yes	characteristic
11	#13063443	—	8	2	no	—
12	C₄×D₁₇₃	D₈	1	1	yes	characteristic
13	#13063436	Q₁₆	1	1	yes	characteristic
14	C₈×C₁₇₃	C₄⋊C₄	1	1	yes	characteristic
15	C₂×D₁₇₃	Q₃₂	1	1	yes	characteristic
16	C₄×C₁₇₃	#107	1	1	yes	characteristic
17	Dic₁₇₃	D₁₆	1	1	yes	characteristic
18	C₂×C₁₇₃	#366	1	1	yes	characteristic
19	D₁₇₃	—	2	1	no	—
20	C₁₇₃	#1425	1	1	yes	characteristic, complemented, Sylow
21	#1425	—	173	1	no	maximal, Sylow
22	C₂×C₃₂	—	173	1	no	—
23	#368	—	173	2	no	—
24	C₂×C₁₆	—	173	1	no	—
25	#108	—	346	2	no	—
26	C₃₂	—	173	1	no	—
27	C₃₂	#10621924	1	1	yes	characteristic
28	M₁₆	—	692	2	no	—
29	C₂×C₈	—	173	1	no	—
30	C₁₆	—	173	1	no	—
31	C₁₆	C₂×#10621924	1	1	yes	characteristic
32	C₂×C₄	—	173	1	no	—
33	C₈	—	1384	2	no	—
34	C₈	—	173	1	no	—
35	C₈	C₄⋊#10621924	1	1	yes	characteristic
36	C₂²	—	173	1	no	—
37	C₄	—	173	1	no	—
38	C₄	#19149748	1	1	yes	characteristic
39	C₂	—	346	1	no	—
40	C₂	#26012417	1	1	yes	characteristic

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

N	H ≅ G/N	type
20. C₁₇₃	#1425	semidirect

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