Subgroups — #36373964

Order 22336.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26013579	C₂	1	1	yes	maximal, characteristic
2	C₈×Dic₃₄₉	C₂	1	1	yes	maximal, characteristic
3	M₃₂×C₃₄₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#14584095	C₄	1	1	yes	characteristic
5	C₄×Dic₃₄₉	C₄	1	1	yes	characteristic
6	#19150208	—	2	1	no	—
7	C₂×C₈×C₃₄₉	C₂²	1	1	yes	characteristic
8	C₁₆×C₃₄₉	—	2	1	no	—
9	C₂×Dic₃₄₉	—	2	1	no	—
10	#14584095	C₈	1	2	yes	—
11	C₂×C₄×C₃₄₉	C₂×C₄	1	1	yes	characteristic
12	C₈×C₃₄₉	D₄	1	1	yes	characteristic
13	C₈×C₃₄₉	Q₈	1	1	yes	characteristic
14	C₂²×C₃₄₉	M₁₆	1	1	yes	characteristic
15	C₄×C₃₄₉	C₄⋊C₄	1	1	yes	characteristic
16	C₄×C₃₄₉	C₂×C₈	1	1	yes	characteristic
17	Dic₃₄₉	—	2	2	no	—
18	C₂×C₃₄₉	—	2	1	no	—
19	C₂×C₃₄₉	C₄⋊C₈	1	1	yes	characteristic
20	C₃₄₉	#364	1	1	yes	characteristic, complemented, Sylow
21	#364	—	349	1	no	maximal, Sylow
22	M₃₂	—	349	1	no	—
23	M₃₂	D₃₄₉	1	1	yes	characteristic
24	C₄×C₈	—	349	1	no	—
25	C₂×C₈	—	349	1	no	—
26	C₂×C₈	C₂×D₃₄₉	1	1	yes	characteristic
27	C₄²	—	349	1	no	—
28	C₁₆	—	2	1	no	—
29	C₁₆	—	698	1	no	—
30	C₂×C₄	—	698	1	no	—
31	C₂×C₄	C₄×D₃₄₉	1	1	yes	characteristic
32	C₈	—	349	2	no	—
33	C₈	C₂²⋊D₃₄₉	1	1	yes	characteristic
34	C₈	Dic₆₉₈	1	1	yes	characteristic
35	C₂²	#19150216	1	1	yes	characteristic
36	C₄	—	698	2	no	—
37	C₄	#19150212	1	1	yes	characteristic
38	C₄	C₈×D₃₄₉	1	1	yes	characteristic
39	C₂	—	2	1	no	—
40	C₂	#26013568	1	1	yes	characteristic

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

N	H ≅ G/N	type
20. C₃₄₉	#364	semidirect

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