Subgroups — #36375068

Order 22336.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26013709	C₂	1	1	yes	maximal, characteristic
2	#26013707	C₂	1	1	yes	maximal, characteristic
3	#26013578	C₂	1	1	yes	maximal, characteristic
4	#19150243	—	2	1	no	—
5	C₄⋊#13063703	—	2	1	no	—
6	C₈×D₃₄₉	C₂²	1	1	yes	characteristic
7	#19150208	C₄	1	1	yes	characteristic, complemented
8	C₁₆×C₃₄₉	C₄	1	1	yes	characteristic, complemented
9	C₂×#13063703	—	4	1	no	—
10	#14584102	—	4	1	no	—
11	C₄×D₃₄₉	D₄	1	1	yes	characteristic
12	#14584095	Q₈	1	1	yes	characteristic
13	C₈×C₃₄₉	C₂×C₄	1	1	yes	characteristic
14	C₂×D₃₄₉	SD₁₆	1	1	yes	characteristic
15	#13063703	—	8	1	no	—
16	C₄×C₃₄₉	C₄⋊C₄	1	1	yes	characteristic
17	Dic₃₄₉	SD₁₆	1	1	yes	characteristic
18	C₂×C₃₄₉	#106	1	1	yes	characteristic
19	D₃₄₉	—	2	1	no	—
20	C₃₄₉	#365	1	1	yes	characteristic, complemented, Sylow
21	#365	—	349	1	no	maximal, Sylow
22	M₃₂	—	349	1	no	—
23	#108	—	349	1	no	—
24	#106	—	349	1	no	—
25	M₁₆	—	698	1	no	—
26	C₂×C₈	—	349	1	no	—
27	C₄⋊C₄	—	698	1	no	—
28	C₁₆	—	349	1	no	—
29	C₁₆	#13063703	1	1	yes	characteristic, complemented
30	C₂×C₄	—	349	1	no	—
31	C₂×C₄	—	1396	1	no	—
32	C₈	—	349	1	no	—
33	C₈	—	1396	1	no	—
34	C₈	C₂×#13063703	1	1	yes	characteristic
35	C₂²	—	349	1	no	—
36	C₄	—	349	1	no	—
37	C₄	—	2792	1	no	—
38	C₄	C₄⋊#13063703	1	1	yes	characteristic
39	C₂	—	698	1	no	—
40	C₂	#26013707	1	1	yes	characteristic

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

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