Subgroups — #36368732

Order 22144.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26012330	C₂	1	2	yes	maximal, complemented
2	C₂×#19149585	C₂	1	1	yes	maximal, characteristic
3	#19149585	C₄	1	1	yes	characteristic
4	#19149585	C₂²	1	1	yes	characteristic
5	C₂×C₁₆×C₁₇₃	C₄	1	1	yes	characteristic
6	C₂×C₈×C₁₇₃	C₈	1	1	yes	characteristic
7	C₁₆×C₁₇₃	C₈	1	1	yes	characteristic
8	C₁₆×C₁₇₃	C₂×C₄	1	1	yes	characteristic
9	C₂×C₄×C₁₇₃	C₁₆	1	1	yes	characteristic
10	C₈×C₁₇₃	C₁₆	1	1	yes	characteristic
11	C₈×C₁₇₃	C₂×C₈	1	1	yes	characteristic
12	C₂²×C₁₇₃	C₃₂	1	1	yes	characteristic
13	C₄×C₁₇₃	C₃₂	1	1	yes	characteristic
14	C₄×C₁₇₃	C₂×C₁₆	1	1	yes	characteristic
15	C₂×C₁₇₃	—	2	1	no	—
16	C₂×C₁₇₃	C₂×C₃₂	1	1	yes	characteristic
17	C₁₇₃	M₁₂₈	1	1	yes	characteristic, complemented, Sylow
18	M₁₂₈	—	173	1	no	maximal, Sylow
19	C₂×C₃₂	—	173	1	no	—
20	C₆₄	—	173	2	no	—
21	C₂×C₁₆	#10621924	1	1	yes	characteristic
22	C₃₂	—	173	1	no	—
23	C₃₂	—	173	1	no	—
24	C₂×C₈	#13063443	1	1	yes	characteristic
25	C₁₆	#13063443	1	1	yes	characteristic
26	C₁₆	C₂×#10621924	1	1	yes	characteristic
27	C₂×C₄	#14583829	1	1	yes	characteristic
28	C₈	#14583829	1	1	yes	characteristic
29	C₈	C₂×#13063443	1	1	yes	characteristic
30	C₂²	#19149729	1	1	yes	characteristic
31	C₄	#19149729	1	1	yes	characteristic
32	C₄	C₂×#14583829	1	1	yes	characteristic
33	C₂	—	2	1	no	—
34	C₂	C₂×#19149729	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #26012330	C₂	semidirect
17. C₁₇₃	M₁₂₈	semidirect

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