Subgroups — #36373984

Order 22336.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₂₇₉₂	C₂	1	1	yes	maximal, characteristic
2	#26013545	C₂	1	1	yes	maximal, characteristic
3	Q₃₂×C₃₄₉	C₂	1	1	yes	maximal, characteristic
4	Dic₁₃₉₆	—	2	1	no	—
5	Q₁₆×C₃₄₉	—	2	1	no	—
6	C₁₆×C₃₄₉	C₂²	1	1	yes	characteristic
7	Dic₆₉₈	—	4	1	no	—
8	Q₈×C₃₄₉	—	4	1	no	—
9	C₈×C₃₄₉	D₄	1	1	yes	characteristic
10	C₄×C₃₄₉	—	8	1	no	—
11	C₄×C₃₄₉	D₈	1	1	yes	characteristic
12	Dic₃₄₉	—	8	1	no	—
13	C₂×C₃₄₉	D₁₆	1	1	yes	characteristic
14	C₃₄₉	Q₆₄	1	1	yes	characteristic, complemented, Sylow
15	Q₆₄	—	349	1	no	maximal, Sylow
16	Q₃₂	—	349	1	no	—
17	Q₃₂	D₃₄₉	1	1	yes	characteristic
18	C₃₂	—	349	1	no	—
19	Q₁₆	—	2	1	no	—
20	Q₁₆	—	698	1	no	—
21	C₁₆	C₂×D₃₄₉	1	1	yes	characteristic
22	Q₈	—	4	1	no	—
23	Q₈	—	1396	1	no	—
24	C₈	C₂²⋊D₃₄₉	1	1	yes	characteristic
25	C₄	—	8	1	no	—
26	C₄	—	2792	1	no	—
27	C₄	#19150218	1	1	yes	characteristic
28	C₂	#26013580	1	1	yes	characteristic

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

N	H ≅ G/N	type
14. C₃₄₉	Q₆₄	semidirect

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