Subgroups — #36373966

Order 22336.

42 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	#26013575	C₂	1	1	yes	maximal, characteristic
3	#106×C₃₄₉	C₂	1	1	yes	maximal, characteristic
4	#19150217	—	2	1	no	—
5	#19150208	C₄	1	2	yes	complemented
6	C₂×C₈×C₃₄₉	C₂²	1	1	yes	characteristic
7	C₄⋊C₄×C₃₄₉	—	2	1	no	—
8	#14584095	—	4	1	no	—
9	C₂×C₄×C₃₄₉	—	4	1	no	—
10	C₂×C₄×C₃₄₉	D₄	1	1	yes	characteristic
11	C₈×C₃₄₉	C₂×C₄	1	1	yes	characteristic
12	C₈×C₃₄₉	Q₈	1	1	yes	characteristic
13	C₂²×C₃₄₉	SD₁₆	1	1	yes	characteristic
14	C₄×C₃₄₉	—	8	1	no	—
15	C₄×C₃₄₉	C₄⋊C₄	1	1	yes	characteristic
16	C₄×C₃₄₉	SD₁₆	1	1	yes	characteristic
17	C₂×C₃₄₉	—	2	1	no	—
18	C₂×C₃₄₉	#106	1	1	yes	characteristic
19	C₃₄₉	#365	1	1	yes	characteristic, complemented, Sylow
20	#365	—	349	1	no	maximal, Sylow
21	M₃₂	—	349	1	no	—
22	#108	—	349	1	no	—
23	#106	D₃₄₉	1	1	yes	characteristic
24	M₁₆	—	698	1	no	—
25	C₂×C₈	C₂×D₃₄₉	1	1	yes	characteristic
26	C₄⋊C₄	—	2	1	no	—
27	C₁₆	—	349	2	no	—
28	C₂×C₄	—	4	1	no	—
29	C₂×C₄	C₂²⋊D₃₄₉	1	1	yes	characteristic
30	C₈	—	1396	1	no	—
31	C₈	C₄×D₃₄₉	1	1	yes	characteristic
32	C₈	Dic₆₉₈	1	1	yes	characteristic
33	C₂²	#19150221	1	1	yes	characteristic
34	C₄	—	8	1	no	—
35	C₄	#19150212	1	1	yes	characteristic
36	C₄	#19150220	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#26013570	1	1	yes	characteristic

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

N	H ≅ G/N	type
5. #19150208	C₄	semidirect
19. C₃₄₉	#365	semidirect

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