Subgroups — #36351780

Order 22144.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₂₇₆₈	C₂	1	1	yes	maximal, characteristic
2	#26011210	C₂	1	1	yes	maximal, characteristic
3	Q₆₄×C₁₇₃	C₂	1	1	yes	maximal, characteristic
4	Dic₁₃₈₄	—	2	1	no	—
5	Q₃₂×C₁₇₃	—	2	1	no	—
6	C₃₂×C₁₇₃	C₂²	1	1	yes	characteristic
7	Dic₆₉₂	—	4	1	no	—
8	Q₁₆×C₁₇₃	—	4	1	no	—
9	C₁₆×C₁₇₃	D₄	1	1	yes	characteristic
10	Dic₃₄₆	—	8	1	no	—
11	Q₈×C₁₇₃	—	8	1	no	—
12	C₈×C₁₇₃	D₈	1	1	yes	characteristic
13	C₄×C₁₇₃	—	16	1	no	—
14	C₄×C₁₇₃	D₁₆	1	1	yes	characteristic
15	Dic₁₇₃	—	16	1	no	—
16	C₂×C₁₇₃	D₃₂	1	1	yes	characteristic
17	C₁₇₃	Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
18	Q₁₂₈	—	173	1	no	maximal, Sylow
19	Q₆₄	—	173	1	no	—
20	Q₆₄	D₁₇₃	1	1	yes	characteristic
21	C₆₄	—	173	1	no	—
22	Q₃₂	—	2	1	no	—
23	Q₃₂	—	346	1	no	—
24	C₃₂	C₂×D₁₇₃	1	1	yes	characteristic
25	Q₁₆	—	4	1	no	—
26	Q₁₆	—	692	1	no	—
27	C₁₆	C₂²⋊D₁₇₃	1	1	yes	characteristic
28	Q₈	—	8	1	no	—
29	Q₈	—	1384	1	no	—
30	C₈	#14583811	1	1	yes	characteristic
31	C₄	—	16	1	no	—
32	C₄	—	2768	1	no	—
33	C₄	#19149620	1	1	yes	characteristic
34	C₂	#26011326	1	1	yes	characteristic

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

N	H ≅ G/N	type
17. C₁₇₃	Q₁₂₈	semidirect

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