Subgroups — #36375005

Order 22336.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#14584102	C₂	1	2	yes	maximal
2	C₈×Dic₃₄₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#14584102	—	2	2	no	—
4	C₂×#14584095	C₄	1	1	yes	characteristic
5	C₄×Dic₃₄₉	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₃₄₉	C₄	1	1	yes	characteristic
7	#14584102	—	4	2	no	—
8	C₂×Dic₃₄₉	D₄	1	1	yes	characteristic
9	C₂×Dic₃₄₉	Q₈	1	1	yes	characteristic
10	#14584095	—	2	1	no	—
11	C₂×C₄×C₃₄₉	C₂×C₄	1	1	yes	characteristic
12	C₈×C₃₄₉	C₈	1	2	yes	complemented
13	C₂²×C₃₄₉	C₄⋊C₄	1	1	yes	characteristic
14	C₄×C₃₄₉	C₂×C₈	1	1	yes	characteristic
15	C₄×C₃₄₉	M₁₆	1	1	yes	characteristic
16	Dic₃₄₉	—	2	1	no	—
17	Dic₃₄₉	SD₁₆	1	2	yes	—
18	C₂×C₃₄₉	C₄⋊C₈	1	1	yes	characteristic
19	C₂×C₃₄₉	#106	1	1	yes	characteristic
20	C₂×C₃₄₉	#108	1	1	yes	characteristic
21	C₃₄₉	#334	1	1	yes	characteristic, complemented, Sylow
22	#334	—	349	1	no	maximal, Sylow
23	C₄⋊C₈	—	349	2	no	—
24	C₄×C₈	—	349	1	no	—
25	C₂×C₈	—	349	1	no	—
26	C₂×C₈	—	698	2	no	—
27	C₂×C₈	#13063703	1	1	yes	characteristic
28	C₄²	—	349	1	no	—
29	C₂×C₄	—	349	1	no	—
30	C₂×C₄	—	349	1	no	—
31	C₂×C₄	C₂×#13063703	1	1	yes	characteristic
32	C₈	—	1396	2	no	—
33	C₈	—	698	1	no	—
34	C₈	#14584102	1	2	yes	complemented
35	C₂²	C₄⋊#13063703	1	1	yes	characteristic
36	C₄	—	349	2	no	—
37	C₄	—	698	1	no	—
38	C₄	C₂×#14584102	1	1	yes	characteristic
39	C₄	#19150243	1	1	yes	characteristic
40	C₂	C₄⋊#14584102	1	1	yes	characteristic
41	C₂	#26013707	1	1	yes	characteristic
42	C₂	#26013709	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.