Subgroups — #36375054

Order 22336.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26013700	C₂	1	2	yes	maximal
2	#26013637	C₂	1	1	yes	maximal, characteristic
3	#19150242	—	2	2	no	—
4	C₂×Dic₆₉₈	C₂²	1	1	yes	characteristic
5	#19150212	—	2	2	no	—
6	C₄×Dic₃₄₉	C₄	1	1	yes	characteristic
7	C₂×Q₈×C₃₄₉	C₄	1	1	yes	characteristic
8	#14584102	—	4	2	no	—
9	Dic₆₉₈	—	4	1	no	—
10	C₂×Dic₃₄₉	—	2	1	no	—
11	C₂×Dic₃₄₉	D₄	1	2	yes	—
12	Q₈×C₃₄₉	—	4	1	no	—
13	C₂×C₄×C₃₄₉	—	2	1	no	—
14	C₂×C₄×C₃₄₉	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₃₄₉	C₂²⋊C₄	1	1	yes	characteristic
16	C₄×C₃₄₉	—	2	1	no	—
17	C₄×C₃₄₉	—	4	1	no	—
18	Dic₃₄₉	—	2	2	no	—
19	Dic₃₄₉	—	2	2	no	—
20	C₂×C₃₄₉	—	2	1	no	—
21	C₂×C₃₄₉	#99	1	1	yes	characteristic
22	C₃₄₉	#356	1	1	yes	characteristic, complemented, Sylow
23	#356	—	349	1	no	maximal, Sylow
24	C₄⋊Q₈	—	349	1	no	—
25	#101	—	349	2	no	—
26	C₂×Q₈	—	349	1	no	—
27	C₂×Q₈	#13063703	1	1	yes	characteristic
28	M₁₆	—	698	2	no	—
29	C₄⋊C₄	—	698	2	no	—
30	C₄²	—	349	1	no	—
31	Q₈	—	4	1	no	—
32	Q₈	—	1396	1	no	—
33	C₂×C₄	—	2	1	no	—
34	C₂×C₄	—	349	2	no	—
35	C₂×C₄	—	698	1	no	—
36	C₂×C₄	C₂×#13063703	1	1	yes	characteristic
37	C₈	—	1396	2	no	—
38	C₂²	C₂²⋊#13063703	1	1	yes	characteristic
39	C₄	—	2	1	no	—
40	C₄	—	4	1	no	—
41	C₄	—	698	2	no	—
42	C₄	—	698	2	no	—
43	C₂	—	2	1	no	—
44	C₂	#26013697	1	1	yes	characteristic

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

N	H ≅ G/N	type
22. C₃₄₉	#356	semidirect

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