Subgroups — #36373886

Order 22336.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26013550	C₂	1	2	yes	maximal
2	#125×C₃₄₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#14584095	—	2	2	no	—
4	C₄⋊C₄×C₃₄₉	—	2	2	no	—
5	C₄⋊C₄×C₃₄₉	C₄	1	2	yes	—
6	C₄²×C₃₄₉	C₂²	1	1	yes	characteristic
7	#14584095	—	2	4	no	—
8	C₂×C₄×C₃₄₉	—	2	2	no	—
9	C₂×C₄×C₃₄₉	C₂×C₄	1	1	yes	characteristic
10	C₂×C₄×C₃₄₉	D₄	1	2	yes	—
11	C₂²×C₃₄₉	C₂²⋊C₄	1	1	yes	characteristic
12	C₄×C₃₄₉	—	2	1	no	—
13	C₄×C₃₄₉	—	2	2	no	—
14	C₄×C₃₄₉	—	4	2	no	—
15	C₂×C₃₄₉	#101	1	1	yes	characteristic
16	C₂×C₃₄₉	#104	1	2	yes	—
17	C₃₄₉	#330	1	1	yes	characteristic, complemented, Sylow
18	#330	—	349	1	no	maximal, Sylow
19	#125	D₃₄₉	1	1	yes	characteristic
20	#97	—	349	2	no	—
21	C₂×C₈	—	698	2	no	—
22	C₄⋊C₄	—	2	2	no	—
23	C₄⋊C₄	Dic₃₄₉	1	2	yes	—
24	C₄²	C₂×D₃₄₉	1	1	yes	characteristic
25	C₂×C₄	—	2	2	no	—
26	C₂×C₄	C₂×Dic₃₄₉	1	1	yes	characteristic
27	C₂×C₄	C₂²⋊D₃₄₉	1	2	yes	—
28	C₈	—	698	4	no	—
29	C₂²	C₂²⋊Dic₃₄₉	1	1	yes	characteristic
30	C₄	—	2	1	no	—
31	C₄	—	2	2	no	—
32	C₄	—	4	2	no	—
33	C₂	#26013558	1	1	yes	characteristic
34	C₂	#26013566	1	2	yes	—

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

N	H ≅ G/N	type
17. C₃₄₉	#330	semidirect

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