Subgroups — #14272096

Order 1856.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₆×D₂₉	C₂	1	1	yes	maximal, characteristic
2	#11745144	C₂	1	2	yes	maximal, complemented
3	C₈×D₂₉	C₄	1	1	yes	characteristic
4	C₁₆×C₂₉	C₄	1	1	yes	characteristic
5	#90768	C₂²	1	1	yes	characteristic
6	C₄×D₂₉	C₈	1	1	yes	characteristic
7	C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
8	#6597	C₈	1	1	yes	characteristic
9	C₂×D₂₉	C₁₆	1	1	yes	characteristic
10	C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
11	Dic₂₉	C₁₆	1	1	yes	characteristic
12	M₆₄	—	29	1	no	maximal, Sylow
13	C₂×C₂₉	C₂×C₁₆	1	1	yes	characteristic
14	D₂₉	—	2	1	no	—
15	C₂×C₁₆	—	29	1	no	—
16	C₃₂	—	29	2	no	—
17	C₂₉	M₆₄	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₈	—	29	1	no	—
19	C₁₆	—	29	1	no	—
20	C₁₆	#1181	1	1	yes	characteristic
21	C₂×C₄	—	29	1	no	—
22	C₈	—	29	1	no	—
23	C₈	C₂×#1181	1	1	yes	characteristic
24	C₂²	—	29	1	no	—
25	C₄	—	29	1	no	—
26	C₄	D₂₉⋊C₈	1	1	yes	characteristic
27	C₂	—	58	1	no	—
28	C₂	D₂₉⋊C₁₆	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. #11745144	C₂	semidirect
17. C₂₉	M₆₄	semidirect

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