Subgroups — #26012549

Order 11072.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19149753	C₂	1	3	yes	maximal, complemented
2	C₂×#14583829	C₂	1	3	yes	maximal, complemented
3	#19149686	C₂	1	1	yes	maximal, characteristic
4	#14583829	C₂²	1	1	yes	characteristic
5	#14583829	C₂²	1	3	yes	—
6	#14583810	C₄	1	3	yes	—
7	C₂×#13063436	C₂²	1	3	yes	—
8	#41×C₁₇₃	C₄	1	1	yes	characteristic
9	#13063436	C₂×C₄	1	3	yes	—
10	#13063436	C₂³	1	1	yes	characteristic
11	Q₈×C₁₇₃	C₈	1	1	yes	characteristic
12	D₄×C₁₇₃	C₈	1	3	yes	—
13	C₂×C₄×C₁₇₃	C₂×C₄	1	3	yes	—
14	C₂²×C₁₇₃	C₂×C₈	1	3	yes	—
15	C₄×C₁₇₃	C₂×C₈	1	3	yes	—
16	C₄×C₁₇₃	C₂²×C₄	1	1	yes	characteristic
17	C₂×C₁₇₃	—	2	3	no	—
18	C₂×C₁₇₃	C₂²×C₈	1	1	yes	characteristic
19	C₁₇₃	#504	1	1	yes	characteristic, complemented, Sylow
20	#504	—	173	1	no	maximal, Sylow
21	#131	—	173	1	no	—
22	M₃₂	—	173	3	no	—
23	C₂×C₁₆	—	173	3	no	—
24	#41	#10621924	1	1	yes	characteristic
25	M₁₆	—	173	3	no	—
26	C₂×C₈	—	173	3	no	—
27	C₁₆	—	173	1	no	—
28	C₁₆	—	173	3	no	—
29	Q₈	#13063443	1	1	yes	characteristic
30	D₄	#13063443	1	3	yes	—
31	C₂×C₄	C₂×#10621924	1	3	yes	—
32	C₈	—	173	3	no	—
33	C₈	—	173	1	no	—
34	C₂²	C₂×#13063443	1	3	yes	—
35	C₄	C₂×#13063443	1	3	yes	—
36	C₄	C₂²×#10621924	1	1	yes	characteristic
37	C₂	—	2	3	no	—
38	C₂	C₂²×#13063443	1	1	yes	characteristic

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

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