Subgroups — #36373893

Order 22336.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#14584095	C₂	1	2	yes	maximal
2	C₄⋊Q₈×C₃₄₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#14584095	—	2	2	no	—
4	C₂×Q₈×C₃₄₉	C₄	1	2	yes	—
5	C₄⋊C₄×C₃₄₉	—	2	2	no	—
6	C₄²×C₃₄₉	C₂²	1	1	yes	characteristic
7	#14584095	—	4	2	no	—
8	Q₈×C₃₄₉	—	4	2	no	—
9	C₂×C₄×C₃₄₉	—	2	2	no	—
10	C₂×C₄×C₃₄₉	C₂×C₄	1	1	yes	characteristic
11	C₂×C₄×C₃₄₉	D₄	1	2	yes	—
12	C₂²×C₃₄₉	C₂²⋊C₄	1	1	yes	characteristic
13	C₄×C₃₄₉	—	2	1	no	—
14	C₄×C₃₄₉	—	4	2	no	—
15	C₄×C₃₄₉	SD₁₆	1	2	yes	—
16	C₄×C₃₄₉	Q₁₆	1	2	yes	—
17	C₂×C₃₄₉	#100	1	1	yes	characteristic
18	C₂×C₃₄₉	#103	1	2	yes	—
19	C₃₄₉	#333	1	1	yes	characteristic, complemented, Sylow
20	#333	—	349	1	no	maximal, Sylow
21	C₄⋊Q₈	D₃₄₉	1	1	yes	characteristic
22	C₄⋊C₈	—	349	2	no	—
23	C₂×Q₈	Dic₃₄₉	1	2	yes	—
24	C₂×C₈	—	698	2	no	—
25	C₄⋊C₄	—	2	2	no	—
26	C₄²	C₂×D₃₄₉	1	1	yes	characteristic
27	Q₈	—	4	2	no	—
28	C₂×C₄	—	2	2	no	—
29	C₂×C₄	C₂×Dic₃₄₉	1	1	yes	characteristic
30	C₂×C₄	C₂²⋊D₃₄₉	1	2	yes	—
31	C₈	—	1396	2	no	—
32	C₂²	C₂²⋊Dic₃₄₉	1	1	yes	characteristic
33	C₄	—	2	1	no	—
34	C₄	—	4	2	no	—
35	C₄	#19150220	1	2	yes	—
36	C₄	#19150223	1	2	yes	—
37	C₂	#26013556	1	1	yes	characteristic
38	C₂	#26013563	1	2	yes	—

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

N	H ≅ G/N	type
19. C₃₄₉	#333	semidirect

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