Subgroups — #36373981

Order 22336.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₅₈₄	C₂	1	1	yes	maximal, characteristic
2	#26013545	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₃₂×C₃₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₂₇₉₂	—	2	1	no	—
5	Q₁₆×C₃₄₉	—	2	1	no	—
6	C₁₆×C₃₄₉	C₂²	1	1	yes	characteristic
7	D₁₃₉₆	—	4	1	no	—
8	Q₈×C₃₄₉	—	4	1	no	—
9	C₈×C₃₄₉	D₄	1	1	yes	characteristic
10	C₂×D₃₄₉	—	8	1	no	—
11	C₄×C₃₄₉	—	8	1	no	—
12	C₄×C₃₄₉	D₈	1	1	yes	characteristic
13	C₂×C₃₄₉	D₁₆	1	1	yes	characteristic
14	D₃₄₉	—	16	1	no	—
15	C₃₄₉	SD₆₄	1	1	yes	characteristic, complemented, Sylow
16	SD₆₄	—	349	1	no	maximal, Sylow
17	Q₃₂	D₃₄₉	1	1	yes	characteristic, complemented
18	D₁₆	—	349	1	no	—
19	C₃₂	—	349	1	no	—
20	Q₁₆	—	2	1	no	—
21	D₈	—	698	1	no	—
22	C₁₆	C₂×D₃₄₉	1	1	yes	characteristic
23	Q₈	—	4	1	no	—
24	D₄	—	1396	1	no	—
25	C₈	C₂²⋊D₃₄₉	1	1	yes	characteristic
26	C₂²	—	2792	1	no	—
27	C₄	—	8	1	no	—
28	C₄	#19150218	1	1	yes	characteristic
29	C₂	—	5584	1	no	—
30	C₂	#26013580	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.