Subgroups — #36351480

Order 22144.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#14583801	C₂	1	2	yes	maximal
2	C₈²×C₁₇₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#14583801	C₄	1	4	yes	—
4	C₄×C₈×C₁₇₃	C₄	1	2	yes	—
5	C₄×C₈×C₁₇₃	C₂²	1	1	yes	characteristic
6	#14583801	C₈	1	8	yes	complemented
7	C₂×C₈×C₁₇₃	C₈	1	4	yes	—
8	C₂×C₈×C₁₇₃	C₂×C₄	1	2	yes	—
9	C₄²×C₁₇₃	C₂×C₄	1	1	yes	characteristic
10	C₂×C₄×C₁₇₃	C₄²	1	1	yes	characteristic
11	C₂×C₄×C₁₇₃	C₂×C₈	1	2	yes	—
12	C₈×C₁₇₃	—	2	4	no	—
13	C₈×C₁₇₃	C₂×C₈	1	4	yes	—
14	C₂²×C₁₇₃	C₄×C₈	1	1	yes	characteristic
15	C₄×C₁₇₃	C₄×C₈	1	2	yes	—
16	C₄×C₁₇₃	M₃₂	1	4	yes	—
17	C₂×C₁₇₃	C₈²	1	1	yes	characteristic
18	C₂×C₁₇₃	#346	1	2	yes	—
19	C₁₇₃	#1311	1	1	yes	characteristic, complemented, Sylow
20	#1311	—	173	1	no	maximal, Sylow
21	C₄×C₁₆	—	173	2	no	—
22	C₈²	D₁₇₃	1	1	yes	characteristic
23	C₂×C₁₆	—	173	4	no	—
24	C₄×C₈	Dic₁₇₃	1	2	yes	—
25	C₄×C₈	C₂×D₁₇₃	1	1	yes	characteristic
26	C₂×C₈	#13063436	1	4	yes	—
27	C₂×C₈	C₄×D₁₇₃	1	2	yes	—
28	C₄²	C₂×Dic₁₇₃	1	1	yes	characteristic
29	C₁₆	—	173	8	no	—
30	C₂×C₄	C₄×Dic₁₇₃	1	1	yes	characteristic
31	C₂×C₄	C₂×#13063436	1	2	yes	—
32	C₈	—	2	4	no	—
33	C₈	C₈×D₁₇₃	1	4	yes	—
34	C₂²	C₄×#13063436	1	1	yes	characteristic
35	C₄	C₈×Dic₁₇₃	1	2	yes	—
36	C₄	#19149619	1	4	yes	—
37	C₂	C₈×#13063436	1	1	yes	characteristic
38	C₂	#26011267	1	2	yes	—

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

N	H ≅ G/N	type
6. #14583801	C₈	semidirect
19. C₁₇₃	#1311	semidirect

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